-
非晶态物质的本质及形成过程是凝聚态物理领域最困难也是最有趣的问题之一. 非晶形成过程在原子结构上不会衍生出人们在传统晶体结构里所熟悉的长程有序性, 因此对于此类在自然界中广泛存在的物质形态, 至今还没有有效的实验表征手段和理论研究方法. 非晶态物质的原子结构及其构效关系的研究是凝聚态物理和材料科学等众多研究领域所关注的热点问题之一. 随着对非晶态物质物性研究的深入, 人们逐渐意识到非晶态物质中原子中程序对系统性质的重要影响, 建立以中程序为基础的结构-动力学关系对于理解玻璃及玻璃转变的本质起着重要的作用. 本文简要综述了基于图论提出的原子局域连接度这一新的结构序参量在液体和玻璃的结构及构效关系研究中的应用. 新的结构序参量从过去侧重于关注局域原子团簇的种类和分布, 转移到更加关注某一类具有特殊对称性的原子的空间连接情况, 即更多地尝试从原子中程序的角度来建立非晶态物质中的构效关系. 新的研究结果表明, 局域连接度可与非晶态物质中原子的短时或长时动力学行为、输运方式、以及振动模态等一系列物理性质建立联系.For a long time, it has been well recognized that there exists a deep link between the fast vibrational excitations and the slow diffusive dynamics in glass-forming systems. However, it remains as an open question whether and how the short-time scale dynamics associated with vibrational intrabasin excitations is related to the long-time dynamics associated with diffusive interbasin hoppings. In this paper we briefly review the research progress that addresses this challenge. By identifying a structural order parameter—local connectivity of a particle which is defined as the number of nearest neighbors having the same local spatial symmetry, it is found that the local connectivity can tune and modulate both the short-time vibrational dynamics and the long-time relaxation dynamics of the studied particles in a model of metallic supercooled liquid. Furthermore, it reveals that the local connectivity leads the long-time decay of the correlation functions to change from stretched exponentials to compressed ones, indicating a dynamic crossover from diffusive to hyperdiffusive motions. This is the first time to report that in supercooled liquids the particles with particular spatial symmetry can present a faster-than-exponential relaxation that has so far only been reported in out-of-equilibrium materials. The recent results suggest a structural bridge to link the fast vibrational dynamics to the slow structural relaxation in glass-forming systems and extends the compressed exponential relaxation phenomenon from earlier reported out-of-equilibrium materials to the metastable supercooled liquids.
-
Keywords:
- amorphous alloys /
- supercooled liquids /
- local connectivity /
- relaxation dynamics
[1] Wang W H 2013 Prog. Phys. 33 177
[2] Wang W H 2019 Prog. Mater. Sci. 106 100561
Google Scholar
[3] Li M X, Zhao S F, Lu Z, Hirata A, Wen P, Bai H Y, Chen M, Schroers J, Liu Y, Wang W H 2019 Nature 569 99
Google Scholar
[4] Anderson P W 1995 Science 267 1611
Google Scholar
[5] Debenedetti P G, Stillinger F H 2001 Nature 410 259
Google Scholar
[6] Cheng Y Q, Ma E 2011 Prog. Mater. Sci. 56 379
Google Scholar
[7] 李茂枝 2017 物理学报 66 176107
Google Scholar
Li M Z 2017 Acta Phys. Sin. 66 176107
Google Scholar
[8] 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
[9] Yang X, Liu R, Yang M, Wang W H, Chen K 2016 Phys. Rev. Lett. 116 238003
Google Scholar
[10] Schoenholz S S, Cubuk E D, Sussman D M, Kaxiras E, Liu A J 2016 Nat. Phys. 12 469
Google Scholar
[11] Tong H, Xu N 2014 Phys. Rev. E 90 010401
Google Scholar
[12] Ning L, Liu P, Zong Y, Liu R, Yang M, Chen K 2019 Phys. Rev. Lett. 122 178002
Google Scholar
[13] Li M, Wang C Z, Hao S G, Kramer M J, Ho K M 2009 Phys. Rev. B 80 184201
Google Scholar
[14] Ma D, Stoica A D, Wang X L 2009 Nat. Mater. 8 30
Google Scholar
[15] Liu X J, Xu Y, Hui X, Lu Z P, Li F, Chen G L, Lu J, Liu C T 2010 Phys. Rev. Lett. 105 155501
Google Scholar
[16] 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
[17] Lü Y J, Entel P 2011 Phys. Rev. B 84 104203
Google Scholar
[18] Wu Z W, Li M Z, Wang W H, Liu K X 2015 Nat. Commun. 6 6035
Google Scholar
[19] Pan S, Wu Z W, Wang W H, Li M Z, Xu L 2017 Sci. Rep. 7 39938
Google Scholar
[20] 武振伟, 李茂枝, 徐莉梅, 汪卫华 2017 物理学报 66 176405
Google Scholar
Wu Z W, Li M Z, Xu L M, Wang W H 2017 Acta Phys. Sin. 66 176405
Google Scholar
[21] Liu X J, Wang S D, Wang H, Wu Y, Liu C T, Li M, Lu Z P 2018 Phys. Rev. B 97 134107
Google Scholar
[22] Li F X, Kong J B, Li M Z 2018 Chin. Phys. B 27 056102
Google Scholar
[23] Topological phase transition and topological phases of matter, the Royal Swedish Academy of Sciences https://www.nobel prize.org/uploads/2018/06/advanced-physicsprize2016.pdf [2019-12-10]
[24] Cao Y, Li J, Kou B, Xia C, Li Z, Chen R, Xie H, Xiao T, Kob W, Hong L, Zhang J, Wang Y 2018 Nat. Commun. 9 2911
Google Scholar
[25] Peng H L, Li M Z, Wang W H, Wang C -Z, Ho K M 2010 Appl. Phys. Lett. 96 021901
Google Scholar
[26] Peng H L, Li M Z, Wang W H 2011 Phys. Rev. Lett. 106 135503
Google Scholar
[27] Li M Z 2014 J. Mater. Sci. Technol. 30 551
Google Scholar
[28] Hu Y C, Li F X, Li M Z, Bai H Y, Wang W H 2015 Nat. Commun. 6 8310
Google Scholar
[29] Li F X, Li M Z 2017 J. Appl. Phys. 122 225103
Google Scholar
[30] Wu Z W, Li M Z, Wang W H, Liu K X 2013 Phys. Rev. B 88 054202
Google Scholar
[31] Wu Z W, Li F X, Huo C W, Li M Z, Wang W H, Liu K X 2016 Sci. Rep. 6 35967
Google Scholar
[32] Wu Z W, Li M Z, Wang W H, Song W J, Liu K X 2013 J. Chem. Phys. 138 074502
Google Scholar
[33] Jiang S Q, Wu Z W, Li M Z 2016 J. Chem. Phys. 144 154502
Google Scholar
[34] Zhang H P, Wang F R, Li M Z 2019 J. Phys. Chem. B 123 1149
Google Scholar
[35] Xu L, Kumar P, Buldyrev S V, Chen S H, Poole P H, Sciortino F, Stanley H E 2005 Proc. Natl. Acad. Sci. 102 16558
Google Scholar
[36] Xu L, Buldyrev S V, Angell C A, Stanley H E 2006 Phys. Rev. E 74 31108
Google Scholar
[37] 李任重, 武振伟, 徐莉梅 2017 物理学报 66 176410
Google Scholar
Li R Z, Wu Z W, Xu L M 2017 Acta Phys. Sin. 66 176410
Google Scholar
[38] 孙保安, 王利峰, 邵建华 2017 物理学报 66 178103
Google Scholar
Sun B A, Wang L F, Shao J H 2017 Acta Phys. Sin. 66 178103
Google Scholar
[39] 王峥, 汪卫华 2017 物理学报 66 176103
Google Scholar
Wang Z, Wang W H 2017 Acta Phys. Sin. 66 176103
Google Scholar
[40] 袁晨晨 2017 物理学报 66 176402
Google Scholar
Yuan C C 2017 Acta Phys. Sin. 66 176402
Google Scholar
[41] Lad K N, Jakse N, Pasturel A 2017 J. Chem. Phys. 146 124502
Google Scholar
[42] Mendelev M I, Sordelet D J, Kramer M J 2007 J. Appl. Phys. 102 043501
Google Scholar
[43] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[44] Newman M E J 2003 SIAM Review 45 167
Google Scholar
[45] Kob W, Andersen H C 1995 Phys. Rev. E 51 4626
[46] Kob W, Andersen H C 1995 Phys. Rev. E 52 4134
Google Scholar
[47] Yuan C C, Yang F, Kargl F, Holland-Moritz D, Simeoni G G, Meyer A 2015 Phys. Rev. B 91 214203
[48] Francesco S 2005 J. Stat. Mech. 2005 P05015
[49] Wu Z W, Kob W, Wang W H, Xu L 2018 Nat. Commun. 9 5334
Google Scholar
[50] Zhang L, Zheng J, Wang Y, Zhang L, Jin Z, Hong L, Wang Y, Zhang J 2017 Nat. Commun. 8 67
Google Scholar
[51] 陈科 2017 物理学报 66 178201
Google Scholar
Chen K 2017 Acta Phys. Sin. 66 178201
Google Scholar
[52] Yang J, Wang Y J, Ma E, Zaccone A, Dai L H, Jiang M Q 2019 Phys. Rev. Lett. 122 015501
Google Scholar
[53] Wang L, Ninarello A, Guan P, Berthier L, Szamel G, Flenner E 2019 Nat. Commun. 10 26
Google Scholar
[54] Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200
Google Scholar
[55] Kob W 1999 J. Phys: Condens. Matter 11 R85
Google Scholar
[56] Ruta B, Baldi G, Chushkin Y, Rufflé B, Cristofolini L, Fontana A, Zanatta M, Nazzani F 2014 Nat. Commun. 5 3939
Google Scholar
[57] Ruta B, Baldi G, Scarponi F, Fioretto D, Giordano V M, Monaco G 2012 J. Chem. Phys. 137 214502
Google Scholar
[58] Cipelletti L, Manley S, Ball R C, Weitz D A 2000 Phys. Rev. Lett. 84 2275
Google Scholar
[59] Ballesta P, Duri A, Cipelletti L 2008 Nat. Phys. 4 550
Google Scholar
[60] Caronna C, Chushkin Y, Madsen A, Cupane A 2008 Phys. Rev. Lett. 100 055702
Google Scholar
[61] Guo H, Bourret G, Corbierre M K, Rucareanu S, Lennox R B, Laaziri K, Piche L, Sutton M, Harden J L, Leheny R L 2009 Phys. Rev. Lett. 102 075702
Google Scholar
[62] Angell C A 1995 Science 267 1924
Google Scholar
[63] Horbach J, Kob W, Binder K, Angell C A 1996 Phys. Rev. E 54 R5897
Google Scholar
[64] Kob W, Barrat J-L 1997 Phys. Rev. Lett. 78 4581
Google Scholar
[65] Horbach J, Kob W, Binder K 2001 Eur. Phys. J. B 19 531
Google Scholar
[66] Sastry S, Austen Angell C 2003 Nat. Mater. 2 739
Google Scholar
[67] Sette F, Krisch M H, Masciovecchio C, Ruocco G, Monaco G 1998 Science 280 1550
Google Scholar
[68] Sokolov A P, Rössler E, Kisliuk A, Quitmann D 1993 Phys. Rev. Lett. 71 2062
Google Scholar
[69] Scopigno T, Ruocco G, Sette F, Monaco G 2003 Science 302 849
Google Scholar
[70] Shintani H, Tanaka H 2008 Nat. Mater. 7 870
Google Scholar
[71] Huang B, Zhu Z G, Ge T P, Bai H Y, Sun B A, Yang Y, Liu C T, Wang W H 2016 Acta Mater. 110 73
Google Scholar
[72] Luo P, Li Y Z, Bai H Y, Wen P, Wang W H 2016 Phys. Rev. Lett. 116 175901
Google Scholar
[73] Finney J L 1977 Nature 266 309
Google Scholar
[74] Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419
Google Scholar
[75] Wakeda M, Shibutani Y 2010 Acta Mater 58 3963
Google Scholar
[76] Hansen J, McDonald I 2006 Theory of Simple Liquids (3rd Ed.) (London; Burlingtong, MA: Elsevier Academic Press) p185
[77] Binder K, Kob W 2011 Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics (Revised Edition) (Singapore: World Scientific) pp35−79
[78] Zhang Y, Wang C Z, Zhang F, Mendelev M I, Kramer M J, Ho K M 2014 Appl. Phys. Lett. 105 061905
Google Scholar
[79] Luo P, Wen P, Bai H Y, Ruta B, Wang W H 2017 Phys. Rev. Lett. 118 225901
Google Scholar
[80] Desgranges C, Delhommelle J 2019 Phys. Rev. Lett. 123 195701
Google Scholar
[81] Desgranges C, Delhommelle J 2018 Phys. Rev. Lett. 120 115701
Google Scholar
[82] Bi Q L, Lü Y J, Wang W H 2018 Phys. Rev. Lett. 120 155501
Google Scholar
-
图 11 具有不同k值的粒子的自散射函数(SISF)[49], 图中黑色实线为唯象模型((9)式)的拟合结果, 图的右上角给出SISF曲线的整体形状; 其他类型粒子的SISF曲线也一并在图中给出, 以方便对比
Fig. 11. Short-time behavior of the self-intermediate scattering function of particles with different local connectivity k (symbols)[49]. The wave-vector is q = 2.8 Å–1 and T = 1000 K. The solid lines are fits to the data with Eq. (9). Also included is Fs(q, t) for the Cu atoms in an icosahedral cluster (dashed red line), the Cu atoms not in an icosahedral cluster (blue dashed line), and all Cu atoms (green). The black dashed line is the correlation function averaged over all atoms. The upper inset shows the same data in a larger time interval.
图 13 (a) ωH和ωL与局域连接度k均成正相关关系[49]; (b) 随着k值的增加, 权重因子CL上升而CH降低; (c) 高频模式ωH(q)的波矢q无关性表明其局域模式的特征; (d) ωL(q)所具有的色散关系表明它是一种扩展性质的模式, 图中黑色虚线为相应数据点的线性拟合
Fig. 13. (a) Both the high and low frequency modes, ωH and ωL, increases with increasing k[49]; (b) the fraction of motion CL/H increases for ωL and decreases for ωH; (c) the high frequency mode ωH(q) is approximately q-independent, characteristic of localization of the vibrational modes; (d) the low frequency mode ωL(q) increases monotonically with increasing q, characteristic of collective dynamics.
图 14 (a) 具有不同k值的粒子在q = 2.8 Å–1下的长时动力学弛豫曲线, 图中黑色实线为KWW公式拟合所得[49]; (b) 不同波矢q下的形状因子β与k值的关系, β值的变化预示着动力学行为从拉伸e指数弛豫到压缩e指数形式的转变, 转变的有无及具体位置与波矢q密切相关
Fig. 14. (a) Long-time decay of the correlation functions at q = 2.8 Å–1 for particles with different k values[49]. The black solid lines are the Kohlrausch-Williams-Watt (KWW) fits. (b) The k dependence of the exponent β. The variation of β reveals a dynamic crossover from stretched (β < 1) exponential relaxation to compressed (β > 1) one. It can be seen that the cross-over from stretched to compressed exponential depends on q.
图 15 弛豫时间τ与波矢q之间的关系, 为了更好地区分1/q scaling和1/q2 scaling, 这里把数据重新表述成了qτ与q之间的关系[49]
Fig. 15. Wave vector q dependence of the relaxation time τ of the final decay of Fs(q, t) for particles having different local connectivities[49]. Here we show qτ as a function of q to make it simpler to see the 1/q law and to distinguish it from the 1/q2 law.
-
[1] Wang W H 2013 Prog. Phys. 33 177
[2] Wang W H 2019 Prog. Mater. Sci. 106 100561
Google Scholar
[3] Li M X, Zhao S F, Lu Z, Hirata A, Wen P, Bai H Y, Chen M, Schroers J, Liu Y, Wang W H 2019 Nature 569 99
Google Scholar
[4] Anderson P W 1995 Science 267 1611
Google Scholar
[5] Debenedetti P G, Stillinger F H 2001 Nature 410 259
Google Scholar
[6] Cheng Y Q, Ma E 2011 Prog. Mater. Sci. 56 379
Google Scholar
[7] 李茂枝 2017 物理学报 66 176107
Google Scholar
Li M Z 2017 Acta Phys. Sin. 66 176107
Google Scholar
[8] 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
[9] Yang X, Liu R, Yang M, Wang W H, Chen K 2016 Phys. Rev. Lett. 116 238003
Google Scholar
[10] Schoenholz S S, Cubuk E D, Sussman D M, Kaxiras E, Liu A J 2016 Nat. Phys. 12 469
Google Scholar
[11] Tong H, Xu N 2014 Phys. Rev. E 90 010401
Google Scholar
[12] Ning L, Liu P, Zong Y, Liu R, Yang M, Chen K 2019 Phys. Rev. Lett. 122 178002
Google Scholar
[13] Li M, Wang C Z, Hao S G, Kramer M J, Ho K M 2009 Phys. Rev. B 80 184201
Google Scholar
[14] Ma D, Stoica A D, Wang X L 2009 Nat. Mater. 8 30
Google Scholar
[15] Liu X J, Xu Y, Hui X, Lu Z P, Li F, Chen G L, Lu J, Liu C T 2010 Phys. Rev. Lett. 105 155501
Google Scholar
[16] 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
[17] Lü Y J, Entel P 2011 Phys. Rev. B 84 104203
Google Scholar
[18] Wu Z W, Li M Z, Wang W H, Liu K X 2015 Nat. Commun. 6 6035
Google Scholar
[19] Pan S, Wu Z W, Wang W H, Li M Z, Xu L 2017 Sci. Rep. 7 39938
Google Scholar
[20] 武振伟, 李茂枝, 徐莉梅, 汪卫华 2017 物理学报 66 176405
Google Scholar
Wu Z W, Li M Z, Xu L M, Wang W H 2017 Acta Phys. Sin. 66 176405
Google Scholar
[21] Liu X J, Wang S D, Wang H, Wu Y, Liu C T, Li M, Lu Z P 2018 Phys. Rev. B 97 134107
Google Scholar
[22] Li F X, Kong J B, Li M Z 2018 Chin. Phys. B 27 056102
Google Scholar
[23] Topological phase transition and topological phases of matter, the Royal Swedish Academy of Sciences https://www.nobel prize.org/uploads/2018/06/advanced-physicsprize2016.pdf [2019-12-10]
[24] Cao Y, Li J, Kou B, Xia C, Li Z, Chen R, Xie H, Xiao T, Kob W, Hong L, Zhang J, Wang Y 2018 Nat. Commun. 9 2911
Google Scholar
[25] Peng H L, Li M Z, Wang W H, Wang C -Z, Ho K M 2010 Appl. Phys. Lett. 96 021901
Google Scholar
[26] Peng H L, Li M Z, Wang W H 2011 Phys. Rev. Lett. 106 135503
Google Scholar
[27] Li M Z 2014 J. Mater. Sci. Technol. 30 551
Google Scholar
[28] Hu Y C, Li F X, Li M Z, Bai H Y, Wang W H 2015 Nat. Commun. 6 8310
Google Scholar
[29] Li F X, Li M Z 2017 J. Appl. Phys. 122 225103
Google Scholar
[30] Wu Z W, Li M Z, Wang W H, Liu K X 2013 Phys. Rev. B 88 054202
Google Scholar
[31] Wu Z W, Li F X, Huo C W, Li M Z, Wang W H, Liu K X 2016 Sci. Rep. 6 35967
Google Scholar
[32] Wu Z W, Li M Z, Wang W H, Song W J, Liu K X 2013 J. Chem. Phys. 138 074502
Google Scholar
[33] Jiang S Q, Wu Z W, Li M Z 2016 J. Chem. Phys. 144 154502
Google Scholar
[34] Zhang H P, Wang F R, Li M Z 2019 J. Phys. Chem. B 123 1149
Google Scholar
[35] Xu L, Kumar P, Buldyrev S V, Chen S H, Poole P H, Sciortino F, Stanley H E 2005 Proc. Natl. Acad. Sci. 102 16558
Google Scholar
[36] Xu L, Buldyrev S V, Angell C A, Stanley H E 2006 Phys. Rev. E 74 31108
Google Scholar
[37] 李任重, 武振伟, 徐莉梅 2017 物理学报 66 176410
Google Scholar
Li R Z, Wu Z W, Xu L M 2017 Acta Phys. Sin. 66 176410
Google Scholar
[38] 孙保安, 王利峰, 邵建华 2017 物理学报 66 178103
Google Scholar
Sun B A, Wang L F, Shao J H 2017 Acta Phys. Sin. 66 178103
Google Scholar
[39] 王峥, 汪卫华 2017 物理学报 66 176103
Google Scholar
Wang Z, Wang W H 2017 Acta Phys. Sin. 66 176103
Google Scholar
[40] 袁晨晨 2017 物理学报 66 176402
Google Scholar
Yuan C C 2017 Acta Phys. Sin. 66 176402
Google Scholar
[41] Lad K N, Jakse N, Pasturel A 2017 J. Chem. Phys. 146 124502
Google Scholar
[42] Mendelev M I, Sordelet D J, Kramer M J 2007 J. Appl. Phys. 102 043501
Google Scholar
[43] Plimpton S 1995 J. Comput. Phys. 117 1
Google Scholar
[44] Newman M E J 2003 SIAM Review 45 167
Google Scholar
[45] Kob W, Andersen H C 1995 Phys. Rev. E 51 4626
[46] Kob W, Andersen H C 1995 Phys. Rev. E 52 4134
Google Scholar
[47] Yuan C C, Yang F, Kargl F, Holland-Moritz D, Simeoni G G, Meyer A 2015 Phys. Rev. B 91 214203
[48] Francesco S 2005 J. Stat. Mech. 2005 P05015
[49] Wu Z W, Kob W, Wang W H, Xu L 2018 Nat. Commun. 9 5334
Google Scholar
[50] Zhang L, Zheng J, Wang Y, Zhang L, Jin Z, Hong L, Wang Y, Zhang J 2017 Nat. Commun. 8 67
Google Scholar
[51] 陈科 2017 物理学报 66 178201
Google Scholar
Chen K 2017 Acta Phys. Sin. 66 178201
Google Scholar
[52] Yang J, Wang Y J, Ma E, Zaccone A, Dai L H, Jiang M Q 2019 Phys. Rev. Lett. 122 015501
Google Scholar
[53] Wang L, Ninarello A, Guan P, Berthier L, Szamel G, Flenner E 2019 Nat. Commun. 10 26
Google Scholar
[54] Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200
Google Scholar
[55] Kob W 1999 J. Phys: Condens. Matter 11 R85
Google Scholar
[56] Ruta B, Baldi G, Chushkin Y, Rufflé B, Cristofolini L, Fontana A, Zanatta M, Nazzani F 2014 Nat. Commun. 5 3939
Google Scholar
[57] Ruta B, Baldi G, Scarponi F, Fioretto D, Giordano V M, Monaco G 2012 J. Chem. Phys. 137 214502
Google Scholar
[58] Cipelletti L, Manley S, Ball R C, Weitz D A 2000 Phys. Rev. Lett. 84 2275
Google Scholar
[59] Ballesta P, Duri A, Cipelletti L 2008 Nat. Phys. 4 550
Google Scholar
[60] Caronna C, Chushkin Y, Madsen A, Cupane A 2008 Phys. Rev. Lett. 100 055702
Google Scholar
[61] Guo H, Bourret G, Corbierre M K, Rucareanu S, Lennox R B, Laaziri K, Piche L, Sutton M, Harden J L, Leheny R L 2009 Phys. Rev. Lett. 102 075702
Google Scholar
[62] Angell C A 1995 Science 267 1924
Google Scholar
[63] Horbach J, Kob W, Binder K, Angell C A 1996 Phys. Rev. E 54 R5897
Google Scholar
[64] Kob W, Barrat J-L 1997 Phys. Rev. Lett. 78 4581
Google Scholar
[65] Horbach J, Kob W, Binder K 2001 Eur. Phys. J. B 19 531
Google Scholar
[66] Sastry S, Austen Angell C 2003 Nat. Mater. 2 739
Google Scholar
[67] Sette F, Krisch M H, Masciovecchio C, Ruocco G, Monaco G 1998 Science 280 1550
Google Scholar
[68] Sokolov A P, Rössler E, Kisliuk A, Quitmann D 1993 Phys. Rev. Lett. 71 2062
Google Scholar
[69] Scopigno T, Ruocco G, Sette F, Monaco G 2003 Science 302 849
Google Scholar
[70] Shintani H, Tanaka H 2008 Nat. Mater. 7 870
Google Scholar
[71] Huang B, Zhu Z G, Ge T P, Bai H Y, Sun B A, Yang Y, Liu C T, Wang W H 2016 Acta Mater. 110 73
Google Scholar
[72] Luo P, Li Y Z, Bai H Y, Wen P, Wang W H 2016 Phys. Rev. Lett. 116 175901
Google Scholar
[73] Finney J L 1977 Nature 266 309
Google Scholar
[74] Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419
Google Scholar
[75] Wakeda M, Shibutani Y 2010 Acta Mater 58 3963
Google Scholar
[76] Hansen J, McDonald I 2006 Theory of Simple Liquids (3rd Ed.) (London; Burlingtong, MA: Elsevier Academic Press) p185
[77] Binder K, Kob W 2011 Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics (Revised Edition) (Singapore: World Scientific) pp35−79
[78] Zhang Y, Wang C Z, Zhang F, Mendelev M I, Kramer M J, Ho K M 2014 Appl. Phys. Lett. 105 061905
Google Scholar
[79] Luo P, Wen P, Bai H Y, Ruta B, Wang W H 2017 Phys. Rev. Lett. 118 225901
Google Scholar
[80] Desgranges C, Delhommelle J 2019 Phys. Rev. Lett. 123 195701
Google Scholar
[81] Desgranges C, Delhommelle J 2018 Phys. Rev. Lett. 120 115701
Google Scholar
[82] Bi Q L, Lü Y J, Wang W H 2018 Phys. Rev. Lett. 120 155501
Google Scholar
计量
- 文章访问数: 14922
- PDF下载量: 674
- 被引次数: 0