Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids

Abstract

In crystals, molecules thermally vibrate around the periodic lattice sites. Vibrational motions are well understood in terms of phonons, which carry heat and control heat transport. The situation is notably different in disordered solids, where vibrational excitations are not phonons and can be even localized. Recent numerical work has established the concept of elastic heterogeneity: disordered solids show inhomogeneous local mechanical response. Clearly, the heterogeneous nature of elastic properties strongly influences vibrational and thermal properties, and it is expected to be the origin of anomalous features, including boson peak, vibrational localization, and temperature dependence of thermal conductivity. These are all crucial long-standing problems in materials physics, which we address in the present work. We have considered a toy model able to stabilize different states of matter, by introducing an increasing amount of size disorder. The phase diagram generated by molecular dynamics simulations encompasses the perfect crystalline state with a spatially homogeneous elastic moduli distribution, multiple defective phases with increasing moduli heterogeneities, and eventually a series of amorphous states. We have established clear correlations among the heterogeneous local mechanical response, vibrational states, and thermal conductivity. We provide evidence that elastic heterogeneity controls both vibrational and thermal properties, and is a key concept to understand the anomalous puzzling features of disordered solids.

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• Scaling up the lattice dynamics of amorphous materials by orders of magnitude
• Emergence of linear isotropic elasticity in amorphous and polycrystalline materials
• Analysis of vibrational normal modes for Coulomb clusters
• Variability of mesoscopic mechanical disorder in disordered solids
• Intermittent rearrangements accompanying thermal fluctuations distinguish glasses from crystals
• Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses
• Time correlation functions for quantum systems: validating Bayesian approaches for harmonic oscillators and beyond
• Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition
• Rayleigh anomalies and disorder-induced mixing of polarizations at nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride glass
• Thermal Conductivity of Glass-Forming Liquids
• Selective 3-dimensional patterning during phase separation of a continuously laminated layer
• Critical fluctuations of elastic moduli in jammed solids