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Linking local connectivity to atomic-scale relaxation dynamics in metallic glass-forming systems

Wu Zhen-Wei Wang Wei-Hua

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Linking local connectivity to atomic-scale relaxation dynamics in metallic glass-forming systems

Wu Zhen-Wei, Wang Wei-Hua
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  • 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.
      Corresponding author: Wu Zhen-Wei, zwwu@bnu.edu.cn
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  • 图 1  静态结构因子S(q)的数值计算结果二维示意图 (a)无序结构; (b)有序晶体结构

    Figure 1.  Structure factor S(q) obtained in computer simulation: (a) For disordered structure; (b) for ordered crystal structure.

    图 2  液态Cu50Zr50在1000 K下的静态结构因子S(q) (图中对不同计算方式得到的结果进行了对比)

    Figure 2.  Structure factors S(q) of liquid Cu50Zr50 at 1000 K, obtained with different protocols.

    图 3  图或网络的示例以及它的邻接矩阵[44]

    Figure 3.  A small example graph (or network) with its adjacency matrix[44].

    图 4  CuZr合金中Cu原子和Zr原子在1000 K下的均方位移

    Figure 4.  Mean-square displacement for Cu/Zr atoms in liquid CuZr alloy at 1000 K.

    图 5  相干散射函数F(q, t)和自散射函数Fs(q, t)在不同q下的比较 (a) q = 0.6 Å-1; (b) q = 2.8 Å-1

    Figure 5.  Comparison between F(q, t) and Fs(q, t) at different q values: (a) q = 0.6 Å-1; (b) q = 2.8 Å-1.

    图 6  针对CuZr玻璃的不同粒子数及不同计算方法所获得的振动态密度D(ω)的比较, 及对玻色峰的展示[49]

    Figure 6.  Vibrational density of states for CuZr glass with different protocols, and the test for the present of a boson peak[49].

    图 7  CuZr金属玻璃10 K下通过对其原子的速度自关联函数进行傅里叶变换所得到的振动态密度, 数据表明10 K下系统内部已经几乎不存在可能影响到D(ω)的老化过程

    Figure 7.  Vibrational density of states obtained by calculation of the time Fourier transformation of the velocity auto-correlation function. It can be seen that there is no apparent aging effect at 10 K.

    图 8  局域连接度定义的示意图(指定原子的最近邻原子中, 与指定原子具有相同局域对称性(用相同的颜色表示)的原子的总数即为指定原子的连接度)

    Figure 8.  Illustration of the definition of particles with different connectivities k : Particles in blue are the center of an icosahedral-like cluster.

    图 9  不同温度下二十面体中心原子的连接度的分布[49] (a) T = 1100 K; (b) T = 1000 K; (c) T = 950 K

    Figure 9.  Probability that an icosahedron is of type k[49]: (a) T = 1100 K; (b) T = 1000 K; (c) T = 950 K.

    图 10  Cu50Zr50在不同温度下的静态结构因子S(q)[49]

    Figure 10.  The q-dependence of the partial structure factors for three temperatures considered[49].

    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

    Figure 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 12  具有不同k值原子的振动态密度D(ω)

    Figure 12.  Vibrational density of states of particles with different local connectivity k.

    图 13  (a) ωHωL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

    Figure 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βk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

    Figure 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q之间的关系[49]

    Figure 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 as a function of q to make it simpler to see the 1/q law and to distinguish it from the 1/q2 law.

    图 16  1000 K下标记为不同类型的原子的均方位移曲线[49]

    Figure 16.  Mean squared displacement for different type of atoms at 1000 K[49]

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    Wang W H 2013 Prog. Phys. 33 177

    [2]

    Wang W H 2019 Prog. Mater. Sci. 106 100561Google 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 99Google Scholar

    [4]

    Anderson P W 1995 Science 267 1611Google Scholar

    [5]

    Debenedetti P G, Stillinger F H 2001 Nature 410 259Google Scholar

    [6]

    Cheng Y Q, Ma E 2011 Prog. Mater. Sci. 56 379Google Scholar

    [7]

    李茂枝 2017 物理学报 66 176107Google Scholar

    Li M Z 2017 Acta Phys. Sin. 66 176107Google 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 176112Google 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 176112Google Scholar

    [9]

    Yang X, Liu R, Yang M, Wang W H, Chen K 2016 Phys. Rev. Lett. 116 238003Google Scholar

    [10]

    Schoenholz S S, Cubuk E D, Sussman D M, Kaxiras E, Liu A J 2016 Nat. Phys. 12 469Google Scholar

    [11]

    Tong H, Xu N 2014 Phys. Rev. E 90 010401Google Scholar

    [12]

    Ning L, Liu P, Zong Y, Liu R, Yang M, Chen K 2019 Phys. Rev. Lett. 122 178002Google Scholar

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    Li M, Wang C Z, Hao S G, Kramer M J, Ho K M 2009 Phys. Rev. B 80 184201Google Scholar

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    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 155501Google Scholar

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    Zeng Q, Sheng H, Ding Y, Wang L, Yang W, Jiang J Z, Mao W L, Mao H K 2011 Science 332 1404Google Scholar

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    Lü Y J, Entel P 2011 Phys. Rev. B 84 104203Google Scholar

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    Wu Z W, Li M Z, Wang W H, Liu K X 2015 Nat. Commun. 6 6035Google Scholar

    [19]

    Pan S, Wu Z W, Wang W H, Li M Z, Xu L 2017 Sci. Rep. 7 39938Google Scholar

    [20]

    武振伟, 李茂枝, 徐莉梅, 汪卫华 2017 物理学报 66 176405Google Scholar

    Wu Z W, Li M Z, Xu L M, Wang W H 2017 Acta Phys. Sin. 66 176405Google 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 134107Google Scholar

    [22]

    Li F X, Kong J B, Li M Z 2018 Chin. Phys. B 27 056102Google 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 2911Google Scholar

    [25]

    Peng H L, Li M Z, Wang W H, Wang C -Z, Ho K M 2010 Appl. Phys. Lett. 96 021901Google Scholar

    [26]

    Peng H L, Li M Z, Wang W H 2011 Phys. Rev. Lett. 106 135503Google Scholar

    [27]

    Li M Z 2014 J. Mater. Sci. Technol. 30 551Google Scholar

    [28]

    Hu Y C, Li F X, Li M Z, Bai H Y, Wang W H 2015 Nat. Commun. 6 8310Google Scholar

    [29]

    Li F X, Li M Z 2017 J. Appl. Phys. 122 225103Google Scholar

    [30]

    Wu Z W, Li M Z, Wang W H, Liu K X 2013 Phys. Rev. B 88 054202Google Scholar

    [31]

    Wu Z W, Li F X, Huo C W, Li M Z, Wang W H, Liu K X 2016 Sci. Rep. 6 35967Google Scholar

    [32]

    Wu Z W, Li M Z, Wang W H, Song W J, Liu K X 2013 J. Chem. Phys. 138 074502Google Scholar

    [33]

    Jiang S Q, Wu Z W, Li M Z 2016 J. Chem. Phys. 144 154502Google Scholar

    [34]

    Zhang H P, Wang F R, Li M Z 2019 J. Phys. Chem. B 123 1149Google 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 16558Google Scholar

    [36]

    Xu L, Buldyrev S V, Angell C A, Stanley H E 2006 Phys. Rev. E 74 31108Google Scholar

    [37]

    李任重, 武振伟, 徐莉梅 2017 物理学报 66 176410Google Scholar

    Li R Z, Wu Z W, Xu L M 2017 Acta Phys. Sin. 66 176410Google Scholar

    [38]

    孙保安, 王利峰, 邵建华 2017 物理学报 66 178103Google Scholar

    Sun B A, Wang L F, Shao J H 2017 Acta Phys. Sin. 66 178103Google Scholar

    [39]

    王峥, 汪卫华 2017 物理学报 66 176103Google Scholar

    Wang Z, Wang W H 2017 Acta Phys. Sin. 66 176103Google Scholar

    [40]

    袁晨晨 2017 物理学报 66 176402Google Scholar

    Yuan C C 2017 Acta Phys. Sin. 66 176402Google Scholar

    [41]

    Lad K N, Jakse N, Pasturel A 2017 J. Chem. Phys. 146 124502Google Scholar

    [42]

    Mendelev M I, Sordelet D J, Kramer M J 2007 J. Appl. Phys. 102 043501Google Scholar

    [43]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

    [44]

    Newman M E J 2003 SIAM Review 45 167Google Scholar

    [45]

    Kob W, Andersen H C 1995 Phys. Rev. E 51 4626

    [46]

    Kob W, Andersen H C 1995 Phys. Rev. E 52 4134Google 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 5334Google Scholar

    [50]

    Zhang L, Zheng J, Wang Y, Zhang L, Jin Z, Hong L, Wang Y, Zhang J 2017 Nat. Commun. 8 67Google Scholar

    [51]

    陈科 2017 物理学报 66 178201Google Scholar

    Chen K 2017 Acta Phys. Sin. 66 178201Google Scholar

    [52]

    Yang J, Wang Y J, Ma E, Zaccone A, Dai L H, Jiang M Q 2019 Phys. Rev. Lett. 122 015501Google Scholar

    [53]

    Wang L, Ninarello A, Guan P, Berthier L, Szamel G, Flenner E 2019 Nat. Commun. 10 26Google Scholar

    [54]

    Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200Google Scholar

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    Kob W 1999 J. Phys: Condens. Matter 11 R85Google Scholar

    [56]

    Ruta B, Baldi G, Chushkin Y, Rufflé B, Cristofolini L, Fontana A, Zanatta M, Nazzani F 2014 Nat. Commun. 5 3939Google Scholar

    [57]

    Ruta B, Baldi G, Scarponi F, Fioretto D, Giordano V M, Monaco G 2012 J. Chem. Phys. 137 214502Google Scholar

    [58]

    Cipelletti L, Manley S, Ball R C, Weitz D A 2000 Phys. Rev. Lett. 84 2275Google Scholar

    [59]

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Metrics
  • Abstract views:  13527
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Publishing process
  • Received Date:  10 December 2019
  • Accepted Date:  02 January 2020
  • Published Online:  20 March 2020

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