Equilibrium shape and heterogeneous nucleation barrier at spherical interfaces
Department of Materials Science and Engineering
The conditions for the equilibrium shape of a second-phase particle nucleating either on a spherically curved substrate or at a spherical interphase boundary are derived under the assumption that the spherical interfacial structure has a torque of an appropriate strength. The results are then incorporated into the modified Gibbs-Wulff construction in order to demonstrate a graphical representation of both the equilibrium shape and the free energy barrier for heterogeneous nucleation. The finite curvature associated with the nucleation site causes a geometrical compatibility condition between the radius of the nucleation site and the radius of a critical nucleus, but the compatibility condition vanishes as the ratio of the two radii approaches infinity. Comparison of the free energy barriers for heterogeneous nucleation shows that the free energy of formation, ΔG*, for a critical nucleus on a concave spherical substrate increases with an increase in the radius of the substrate, approaching that of a planar substrate case when the substrate radius becomes infinite. For a spherical interphase boundary, the effect of the curvature is also to decrease ΔG* as the radius of the curvature decreases. On the other hand, ΔG* for the convex spherical substrate case increases as the substrate radius decreases, becoming identical to that of a homogeneous nucleation case when the substrate radius vanishes. However, the condition of a complete wetting, i.e., the condition for a zero ΔG*, remains unaffected by the presence of the finite curvature associated with the nucleation sites.
Equilibrium shape and heterogeneous nucleation barrier at spherical interfaces.
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