Recently we have reported extended simulation work focusing on the concept of elastic heterogeneity in disordered solids. The idea is simple: glasses and disordered (or even very complex) crystals show inhomogeneous mechanical response at the nano-scale, contradicting the macroscopic limit. This property strongly influences vibrational and thermal properties, and could lie at the bottom of the anomalous features of glasses, including boson peak, vibrational localization, and T-dependence of thermal conductivity. 

In order to address the above issues in details and in a unique framework, we have considered a toy model formed by a soft spheres mixture, in fixed high-T/low-ρ conditions. The interesting feature of such a system is that one can stabilize different arrested states by simply tuning continuously the strength of the particles size disorder. Consequently, the phase diagram generated by MD encompasses the perfect crystalline state with a spatially homogeneous elastic moduli distribution, multiple defective phases with increasing moduli heterogeneities, and a series of amorphous states. We have monitored independently mechanical response, collective excitations, and heat transfers across these changes, and established clear correlations among the heterogeneous local mechanical response, the nature of the vibrational states, and the variation of thermal conductivity. In the talk I will focus, in particular, on this latter. 

If time will allow, I will also show that, localizing heterogeneities at interfaces, one can devise ordered materials (super-lattices) with values of thermal conductivity lower than those shown by their amorphous counterpart.