  Effects of three-point direct correlation on properties of the phase field
crystal (PFC) modeling are examined, for the control of various ordered and
disordered phases and their coexistence in both three-dimensional and
two-dimensional systems. Such effects are manifested via the corresponding
gradient nonlinearity in the PFC free energy functional that is derived from
classical density functional theory. Their significant impacts on the stability
regimes of ordered phases, phase diagrams, and elastic properties of the
system, as compared to those of the original PFC model, are revealed through
systematic analyses and simulations. The nontrivial contribution from
three-point direct correlation leads to the variation of the critical point of
order-disorder transition to which all the phase boundaries in the
temperature-density phase diagram converge. It also enables the variation and
control of system elastic constants over a substantial range as needed in
modeling different types of materials with the same crystalline structure but
different elastic properties. The capability of this PFC approach in modeling
both solid and soft matter systems is further demonstrated through the effect
of three-point correlation on controlling the vapor-liquid-solid coexistence
and transitions for body-centered cubic (bcc) phase and on achieving the
liquid-stripe or liquid-lamellar phase coexistence. All these provide a
valuable and efficient method for the study of structural ordering and
evolution in various types of material systems.
