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Line-tension-induced {scenario of heterogeneous nucleation} is studied for alens-shaped nucleus with a finite contact angle nucleated on a sphericalsubstrate and on the bottom of the wall of a spherical cavity. The effect ofline tension on the free energy of a critical nucleus can be separated from theusual volume term. By comparing the free energy of a lens-shaped criticalnucleus of a finite contact angle with that of a spherical nucleus, we findthat a spherical nucleus may have a lower free energy than a lens-shapednucleus when the line tension is positive and large, which is similar to thedrying transition predicted by Widom [B. Widom, J. Phys. Chem. {\bf 99} 2803(1995)]. Then, the homogeneous nucleation rather than the heterogeneousnucleation will be favorable. Similarly, the free energy of a lens-shapednucleus becomes negative when the line tension is negative and large. Then, thebarrier-less nucleation with no thermal activation called athermal nucleationwill be realized.

Line-tension-induced scenario of heterogeneous nucleation on a spherical substrate and in a spherical cavity