玻璃中声激发在介观尺度上的反常性质
Anomalous properties of the acoustic excitations in glasses on the mesoscopic length-scale
摘要：
电介质晶体的低温热性质由具有大波长的声激发控制，所述大波长的声激发由平面波很好地描述。这就是德拜模型，它基于介质是弹性连续体的假设，对于由原子间间距固定的微观尺度上的大声波波长成立，并在接近它时逐渐破裂。玻璃的特征也是普遍的低温热性质，但相对于相应的晶相来说是反常的。相关的普遍异常也出现在低频振动态密度中，尽管存在长期的争论，但仍然知之甚少。使用分子动力学模拟的模型单原子玻璃的尺寸非常大，我们表明，在玻璃中的结构无序破坏德拜模型在一个微妙的方式：弹性连续近似的声学激发突然打破了介观，中程秩序的长度尺度约10个原子间的间距，在那里它仍然适用于相应的晶体系统。在这个尺度上，相对于宏观值，声速显示出明显的减小。这被证明是密切相关的普遍过剩超过德拜模型预测发现在玻璃中的振动态密度的频率为~1太赫兹或在温度为~10 K的比热。
英文摘要：
The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties, that are however anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite of a longstanding debate, still remain poorly understood. Using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: the elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length-scale of about ten interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of ~1 THz in the vibrational density of states or at temperatures of ~10 K in the specific heat.
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