Soft-core particles freezing to form a quasicrystal and a crystal-liquid phase Andrew Archer Alastair M. Rucklidge Edgar Knobloch 2134/18673 https://repository.lboro.ac.uk/articles/journal_contribution/Soft-core_particles_freezing_to_form_a_quasicrystal_and_a_crystal-liquid_phase/9387038 Systems of soft-core particles interacting via a two-scale potential are studied. The potential is responsible for peaks in the structure factor of the liquid state at two different but comparable length scales and a similar bimodal structure is evident in the dispersion relation. Dynamical density functional theory in two dimensions is used to identify two unusual states of this system: a crystal-liquid state, in which the majority of the particles are located on lattice sites but a minority remains free and so behaves like a liquid, and a 12-fold quasicrystalline state. Both are present even for deeply quenched liquids and are found in a regime in which the liquid is unstable with respect to modulations on the smaller scale only. As a result, the system initially evolves towards a small-scale crystal state; this state is not a minimum of the free energy, however, and so the system subsequently attempts to reorganize to generate the lower-energy larger-scale crystals. This dynamical process generates a disordered state with quasicrystalline domains and takes place even when this large scale is linearly stable, i.e., it is a nonlinear process. With controlled initial conditions, a perfect quasicrystal can form. The results are corroborated using Brownian dynamics simulations. 2015-09-09 09:31:11 untagged Mathematical Sciences not elsewhere classified