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

Wu Zhen-Wei; Wang Wei-Hua

doi:10.7498/aps.69.20191870

Abstract

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:

Authors and contacts

Wu Zhen-Wei¹,
Wang Wei-Hua²

1.
School of Systems Science, Beijing Normal University, Beijing 100875, China
2.
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Wu Zhen-Wei, zwwu@bnu.edu.cn

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Cited By

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.

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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.

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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].

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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.

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图 5 相干散射函数F(q, t)和自散射函数F_s(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 F_s(q, t) at different q values: (a) q = 0.6 Å^－1; (b) q = 2.8 Å^－1.

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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].

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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.

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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.

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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.

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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].

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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 F_s(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.

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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.

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图 13 (a) ω_H和ω_L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C_L上升而C_H降低; (c) 高频模式ω_H(q)的波矢q无关性表明其局域模式的特征; (d) ω_L(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, ω_H and ω_L, increases with increasing k^[49]; (b) the fraction of motion C_L/H increases for ω_L and decreases for ω_H; (c) the high frequency mode ω_H(q) is approximately q-independent, characteristic of localization of the vibrational modes; (d) the low frequency mode ω_L(q) increases monotonically with increasing q, characteristic of collective dynamics.

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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

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.

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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]

Figure 15. Wave vector q dependence of the relaxation time τ of the final decay of F_s(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.

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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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map

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Vol. 69, Issue 6 - 2020-03-20

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