  The world of two-dimensional crystals is of great significance for the design
and study of structural and functional materials with novel properties. The
world of two-dimensional crystals is of great significance for the design and
study of structural and functional materials with novel properties. Here we
examine the mechanisms governing the formation and dynamics of these
crystalline or polycrystalline states and their elastic and plastic properties
by constructing a generic multi-mode phase field crystal model. Our results
demonstrate that a system with three competing length scales can order into all
five Bravais lattices, and other more complex structures including honeycomb,
kagome and other hybrid phases. In addition, non-equilibrium phase transitions
are examined to illustrate the complex phase behavior described by the model.
This model provides a systematic path to predict the influence of lattice
symmetry on both structure and dynamics of crystalline and defected systems.
