This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: Sand, powders, and other collections of visible-sized grains are found throughout daily life, from food and pharmaceuticals to soils and industrial materials. When grains of similar size are arranged regularly, they can form a strong crystal-like solid.
Yet what happens inside such an ordered structure immediately before it begins to break has remained unclear. Researchers at the University of Osaka, Shimane University, and Kyoto Sangyo University have now theoretically identified an unusual pattern of vibrations that emerges just before a crystal made of regularly arranged grains yields. Many vibrational modes soften simultaneously along particular directions, while long-wavelength waves travel more slowly than shorter ones.
The findings, published in Physical Review E, reveal a possible physical precursor to failure in highly ordered particulate materials. The team studied a two-dimensional model in which particles were arranged in a triangular crystal and slowly sheared, similar to sliding the top of a deck of cards sideways. By taking advantage of the crystal's regular structure, the researchers analyzed its vibrational modes mathematically as it approached yielding—the point at which deformation becomes irreversible.
Before shear, low-frequency vibrations were concentrated near the center of wavenumber space, corresponding to long wavelengths, as expected for an ordinary solid. Close to yielding, however, soft vibrations extended along two specific directions, forming a cross-shaped pattern in wavenumber space. "Soft" means that even a small force can cause a large vibrational response.
The researchers also found a striking change in how waves travel through the crystal. In ordinary solids, sufficiently long acoustic waves travel at nearly the same speed regardless of wavelength. Immediately before yielding, waves traveling along the soft direction instead followed a quadratic frequency-wavenumber relationship; longer, gentler waves propagated more slowly than shorter ones.
The number of low-frequency vibrations also increased beyond the level predicted by the conventional Debye law. The team derived these relationships analytically, including their numerical prefactors, and confirmed similar behavior using another type of interaction between particles. This suggests that the behavior may occur broadly in defect-free, ordered particulate systems.
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