The phase diagram of hard spheres in a periodic external potential

The density-functional theory has been applied to calculating the phase diagrams of a hard-sphere system in a one-dimensional periodic external potential. The results show that when the wavelength of the external potential is comparable to the hard-sphere solid lattice spacing, the freezing transition occurs at sensitively lower densities. The possibility of a smectic-B-like phase has been investigated in the case of large wavelengths. Two versions of the density-functional theory, the modified weighted-density approximation and generalized effective liquid approximation are shown to give similar phase diagrams.