Origin of the nucleation barrier in athermal hard spheres
Final Report Abstract
Random Close Packing describes the empirical fact that compactifying samples of macroscopic spheres perform a first order phase transition from amorphous to crystalline at a volume fraction of 0.645. The nature of the nucleation barrier responsible for the first order nature is hitherto unknown. Aim of the project is to develop the hypothesis that this nucleation barrier at is kinetic in nature. Our main result is the development of an graph based phase space, where the geometric evolution of the compactifying sphere system can be captured by an advection diffusion type description. We do find a structured flow field of configurations, the characterization of which is ongoing research. The development of our approach was informed by our trials to built a phase space using the Delaunay triangulation. However, this approach can be shown to not capture the relevant mechanics of the system. The same holds true for a characterization of the system using persistent homology. A second result, obtained by new experiments with the setup used by Rietz et al. (2018), is that a confining pressure is not a necessary condition for nucleation. This excludes an alternative theory that had been suggested for the origin of the nucleation barrier.
