Continuum limit of the vibrational properties of amorphous solids
Continuum limit of the vibrational properties of amorphous solids
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DOI：
10.1073/pnas.1709015114
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发表时间：
2017-11-14
影响因子：
11.1
通讯作者：
Ikeda, Atsushi
中科院分区：
文献类型：
--
作者：
Mizuno, Hideyuki;Shiba, Hayato;Ikeda, Atsushi
非晶态固体的低频振动性质和低温热性质与晶态固体有明显的不同。这种情况是违反直觉的，因为所有固体材料都被认为是连续极限下的均匀弹性体，其中振动模式是遵循德拜定律的声子。对于这种情况已经提出了一些唯象的解释，假设弹性不均匀性，软局域振动，等等。微观平均场理论最近已经发展到预测普遍的非德拜标度律。考虑到这些理论论点，绝对有必要直接观察无定形固体低频振动的性质，并确定这种振动所遵循的规律。在这里，我们进行了一个非常大规模的振动模式分析的模型非晶固体。我们发现，平均场理论预测的标度律在低频被违反，在连续极限，振动模式收敛到一个混合的声子模式，遵循德拜定律和软局域模式，遵循另一个普遍的非德拜标度律。
The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomeno-logical explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.