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Line-tension effects on heterogeneous nucleation on a spherical substrate and in a spherical cavity

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.