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In crystals, molecules thermally vibrate around the periodic lattice sites.Vibrational motions are well understood in terms of phonons, which carry heatand control heat transport. The situation is notably different in disorderedsolids, where vibrational excitations are not phonons and can be evenlocalized. Recent numerical work has established the concept of elasticheterogeneity: disordered solids show inhomogeneous local mechanical response.Clearly, the heterogeneous nature of elastic properties strongly influencesvibrational and thermal properties, and it is expected to be the origin ofanomalous features, including boson peak, vibrational localization, andtemperature dependence of thermal conductivity. These are all cruciallong-standing problems in materials physics, which we address in the presentwork. We have considered a toy model able to stabilize different states ofmatter, by introducing an increasing amount of size disorder. The phase diagramgenerated by molecular dynamics simulations encompasses the perfect crystallinestate with a spatially homogeneous elastic moduli distribution, multipledefective phases with increasing moduli heterogeneities, and eventually aseries of amorphous states. We have established clear correlations among theheterogeneous local mechanical response, vibrational states, and thermalconductivity. We provide evidence that elastic heterogeneity controls bothvibrational and thermal properties, and is a key concept to understand theanomalous puzzling features of disordered solids.

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