Crystal Nucleation in Hard Polyhedra Fluids

Self assembly of ordered crystalline structures from monodisperse hard polyhedra leads to a diverse family of crystal structures not accessible in systems of hard spheres including, e.g., the diamond structure.  Although a great deal has been recently discovered regarding the diversity of thermodynamic structures possible, the kinetic process by which these complex structures form has not previously been discussed.  We report results from Monte Carlo simulations using umbrella sampling to determine the free energy barriers required for nucleation of crystals from different polyhedra, and we identify motifs common to their critical nuclei.  We report on the effect of changing particle shape on nucleation barriers.