  The line-tension effects on heterogeneous nucleation are considered when a
spherical lens-shaped nucleus is nucleated on top of a spherical substrate and
on the bottom of the wall of a spherical cavity. The effect of line tension on
the nucleation barrier can be separated from the usual volume term. As the
radius of the substrate increases, the nucleation barrier decreases and
approaches that of a flat substrate. However, as the radius of the cavity
increases, the nucleation barrier increases and approaches that of a flat
substrate. A small spherical substrate is a less active nucleation site than a
flat substrate, and a small spherical cavity is a more active nucleation site
than a flat substrate. In contrast, the line-tension effect on the nucleation
barrier is maximum when the radii of the nucleus and the substrate or cavity
become comparable. Therefore, by tuning the size of the spherical substrate or
spherical cavity, the effect of the line tension can be optimized. These
results will be useful in broad range of applications from material processing
to understanding of global climate, where the heterogeneous nucleation plays a
vital role.
