  We have investigated the melting of nano-sized cone shaped aluminium needles
coated with amorphous carbon using transmission electron microscopy. The
interface between solid and liquid aluminium was found to have spherical
topology. For needles with fixed apex angle, the depressed melting temperature
of this spherical interface, with radius $R$, was found to scale linearly with
the inverse radius $1/R$. However, by varying the apex angle of the needles we
show that the proportionality constant between the depressed melting
temperature and the inverse radius changes significantly. This lead us to the
conclusion that the depressed melting temperature is not controlled solely by
the inverse radius $1/R$. Instead we found a direct relation between the
depressed melting temperature and the ratio between the solid-liquid interface
area and the molten volume.
