Finite size melting of spherical solid-liquid aluminium interfaces

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.