Excess Vibrational Density of States and the Brittle to Ductile Transition in Crystalline and Amorphous Solids

The conditions which determine whether a material behaves in a brittle or ductile fashion on mechanical loading are still elusive and comprise a topic of active research among materials physicists and engineers. In this study, we present results of {\em in silico} mechanical deformation experiments from two very different model solids in two and three dimensions. The first consists of particles interacting with isotropic potentials and the other has strongly direction dependent interactions. We show that in both cases, the excess vibrational density of states is the fundamental quantity which characterises the ductility of the material. Our results can be checked using careful experiments on colloidal solids.