A free-energy functional for a crystal that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function is developed. To test how accurately this free-energy functional describes the symmetry breaking first-order phase transition of freezing, we use it to investigate the crystallization of fluids interacting via the inverse power potential; u(r) = (σ/r) n . In agreement with simulation results we find that under the fluid-solid co-existence the f.c.c. structure is more stable for n = 12, whereas for soft repulsions (n 6) the b.c.c. structure is more stable.

We present a density functional study of Lennard-Jones liquids in contact with a nanocorrugated wall. The corresponding substrate potential is taken to exhibit a repulsive hard core and a Van der Waals attraction. The corrugation is modeled by a periodic array of square nanopits. We have used the modified Rosenfeld density functional in order to study the interfacial structure of these liquids which with respect to their thermodynamic bulk state are considered to be deep inside their liquid phase. We find that already considerably below the packing fraction of bulk freezing of these liquids, inside the nanopits a three-dimensional-like density localization sets in. If the sizes of the pits are commensurate with the packing requirements, we observe high-density spots separated from each other in all spatial directions by liquid of comparatively very low density. The number, shape, size, and density of these high-density spots depend sensitively on the depth and width of the pits. Outside the pits, only layering is observed; above the pit openings these layers are distorted with the distortion reaching up to a few molecular diameters. We discuss quantitatively how this density localization is affected by the geometrical features of the pits and how it evolves upon increasing the bulk packing fraction. Our results are transferable to colloidal systems and pit dimensions corresponding to several diameters of the colloidal particles. For such systems the predicted unfolding of these structural changes can be studied experimentally on much larger length scales and more directly (e.g., optically) than for molecular fluids which typically call for sophisticated x-ray scattering.

A free energy functional for a crystal that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the crystallization of fluids in three-dimensions. The symmetry broken part of the direct pair correlation function has been calculated using a series in ascending powers of the order parameters and which contains three-and higher-bodies direct correlation functions of the isotropic phase. It is shown that a very accurate description of freezing transitions for a wide class of potentials is found by considering the first two terms of this series. The results found for freezing parameters including structure of the frozen phase for fluids interacting via the inverse power potential u(r) = ǫ (σ/r) n for n ranging from 4 to ∞ are in very good agreement with simulation results. It is found that for n > 6.5 the fluid freezes into a face centred cubic (fcc) structure while for n ≤ 6 the body centred cubic (bcc) structure is preferred. The fluid-bcc-fcc triple point is found to be at 1/n = 0.158 which is in good agreement with simulation result.

A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations.We considered amorphous structures found from the molecular dynamics simulations at packing fractions η lower than the glass close packing fraction η J and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile.