Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solids
Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solids
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DOI：
10.1209/0295-5075/90/56001
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
N. Xu;V. Vitelli;Andrea J. Liu;S. Nagel
中科院分区：
文献类型：
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作者：
N. Xu;V. Vitelli;Andrea J. Liu;S. Nagel
我们比较了通过排斥，有限程势相互作用的无摩擦球的三维堵塞包装的振动模式的谐波和非谐波特性。在态密度、扩散率和模的参与率中存在明显的交叉频率。在该频率下，其在干扰阈值处变为零，振动模式具有非常小的参与比，这意味着模式是准本地化的。大多数非谐模式发生在低频，这与晶体中通常发现的情况相反。最低频率模式对压力的响应最强，对机械故障的能量障碍最低。导论. - 理解任何固体的出发点是计算它的谐振动激发。然而，许多重要的性质也需要了解非谐效应。例如，在晶体中，热传输和热膨胀由谐波模式的非谐波耦合控制[1]。当人们考虑固体，无论是晶体还是非晶体，如何分解和失去刚性时，非谐效应变得更加重要。这种行为要求系统在不断越过势能势垒探索不同构型时脱离谐波状态。在本文中，我们讨论了非晶固体的简正模压缩超过干扰阈值的非谐特性和能量障碍。在堵塞过渡时，系统处于固体和液体之间，很不稳定。计算出的这种由软无摩擦球体通过排斥力相互作用组成的固体的振动具有明显的不寻常性质[2]。在德拜谱中，在低频ω处的简正模密度D（ω）在d维中变化为：D（ω）<$ω，而在跃迁堆积分数φc处的态密度有一个一直延伸到零频率的平台。因此，低频模式比简单的平面波激励所能解释的要多得多。在压缩到填充分数φ > φc时，平台持续存在，但仅下降到截止频率ω。对于椭球填料[3]和具有摩擦的系统[4]，也发现了类似的行为。众所周知，模式的各种几何特征强烈依赖于频率[5]。在这里，我们表明，随着频率降低，模式变得越来越异构，低于平均模式协调数。在ω附近，模式开始在空间的小的受限区域中具有高位移振幅。在压缩或施加剪切应力时，当这些模式的频率通过零时，它们最终会使系统不稳定。这些最低频率的模式对粒子重排也有最低的能垒;即使在低温下，它们也可以被充分激发，迫使系统进入不同的构型。在接近无干扰转变时，附近组态之间的势垒缩小到零，因此非谐效应变得更加明显。因此，不仅干扰转变以固体[6]的谐波性质的临界行为为标志，而且还以发散的非谐波效应为标志。
We compare the harmonic and anharmonic properties of the vibrational modes in 3-dimensional jammed packings of frictionless spheres interacting via repulsive, finite range potentials. A crossover frequency is apparent in the density of states, the diffusivity and the participation ratio of the modes. At this frequency, which shifts to zero at the jamming threshold, the vibrational modes have a very small participation ratio implying that the modes are quasi-localized. The most anharmonic modes occur at low frequency which is opposite to what is normally found in crystals. The lowest frequency modes have the strongest response to the pressure and the lowest energy barriers to mechanical failure. Introduction. – A starting point for understanding any solid is a calculation of its harmonic vibrational excitations. However, many important properties require an understanding of anharmonic effects as well. For example, in a crystal, heat transport and thermal expansion are governed by the anharmonic coupling of the harmonic modes [1]. Anharmonic effects become even more essential when one considers how a solid, be it crystalline or amorphous, disintegrates and loses rigidity. Such behavior requires the system to depart from the harmonic regime as it continually moves over potential-energy barriers to explore different configurations. In this paper we discuss the anharmonic properties and energy barriers associated with the normal modes of an amorphous solid compressed above the jamming threshold. At the jamming transition, the system is precariously perched between a solid and a liquid. The vibrations calculated for such a solid composed of soft frictionless spheres interacting via repulsive forces possess decidedly unusual properties [2]. Rather than having a Debye spectrum in which the density of normal modes, D(ω), at low frequency, ω, varies as: D(ω) ∝ ω in d dimensions, the density of states at the transition packing fraction, φc, has a plateau that extends all the way down to zero frequency. Thus, there are many more low-frequency modes than can be accounted for simply by plane-wave excitations. Upon compression to a packing fraction, φ > φc, the plateau persists but only down to a cutoff frequency, ω. Similar behavior is found for ellipsoid packings [3] and systems with friction [4]. It is known that various geometrical features of the modes depend strongly on frequency [5]. Here we show that as the frequency is lowered, the modes become progressively more heterogeneous with a lower-than-average mode coordination number. Near ω, the modes begin to have high displacement amplitudes in small, confined regions of space. Upon compression or application of shear stress, such modes can eventually destabilize the system when their frequency passes through zero. These lowest-frequency modes also have the lowest energy barriers to particle rearrangements; even at low temperature, they can be sufficiently excited to force the system into different configurations. On approaching the unjamming transition, the barriers between nearby configurations shrink to zero so that anharmonic effects become more pronounced. Thus not only is the jamming transition marked by critical behavior in the harmonic properties of the solid [6] but also by diverging anharmonic effects.