Executive Summary : | By introducing and gradually increasing the magnitude of disorder into both crystalline particle packings and crystalline networks, we aim to theoretically study the evolution from crystals to amorphous solids. The evolution of the structures and mechanical properties with increasing disorder will help us understand the physical origin of many peculiar properties of amorphous solids such as the boson peak. This helps build a bridge between the well-established physics of crystals and that of amorphous solids. Such studies can reveal some extraordinary phenomena, including the hidden order-disorder transitions and mechanical metamaterials that possess negative Poisson’s ratios. We plan to develop exact theoretical techniques with which to characterize the fluctuations in positions, forces and interaction energy at the non-equilibrium phase transition between crystals and amorphous solids. |