  I use the method of classical density-functional theory in the
weighted-density approximation of Tarazona to investigate the phase diagram and
the interface structure of a two-dimensional lattice-gas model with three
phases -- vapour, liquid, and triangular solid. While a straightforward
mean-field treatment of the interparticle attraction is unable to give a stable
liquid phase, the correct phase diagram is obtained when including a suitably
chosen square-gradient term in the system grand potential. Taken this theory
for granted, I further examine the structure of the solid-vapour interface as
the triple point is approached from low temperature. Surprisingly, a novel
phase (rather than the liquid) is found to grow at the interface, exhibiting an
unusually long modulation along the interface normal. The conventional
surface-melting behaviour is recovered only by artificially restricting the
symmetries being available to the density field.
