From Crystals to Amorphous Solids Induced by Polydispersity: A Two-Step Melting-Like Transition in Three Dimensions

Starting from crystals, an evolution to amorphous solids occurs with increasing magnitude of particle-size polydispersity η, a process called amorphization transition. The nature of amorphization transition remains unsolved. We try to solve this puzzle by quasistatically increasing and then decreasing polydispersity at η_max in three dimensions, initially from crystals, and observe two well defined transition points η_c and η_d: before η_c, all systems return to crystals with long-range translational and orientational order, after η_d, all systems transform to amorphous solids without any long-range order, and tranform into intermediate states with short-range translational order and long-range orientational order in between.  We argue the analogy between amorphization transition and two-step two-dimensional melting transition. We also observe an increasing number of point defects which are the origin of the loss of long-range translational order in the intermediate states, with increasing η_max. We argue that the point defects break the systems from order to disorder.