Gibbs--Thomson relation

The Gibbs--Thomson relation shifts the equilibrium chemical potential or composition at a curved interface by an amount proportional to its mean curvature. Small droplets therefore have a larger equilibrium solubility than flat interfaces.

For the stipulated spherical solid–liquid capillarity model, $T_m(r)=T_m(\infty )[1-2\gamma /(r\Delta H_V)]$, where $\gamma$ is the interfacial free energy and $\Delta H_V$ the latent heat density. It follows by matching $g_l-g_s\simeq \Delta H_V[T_m(\infty )-T]/T_m(\infty )$ to $2\gamma /r$. Support contacts, free surfaces, anisotropy, premelting and atomistic structure can modify this relation. A continuum extrapolation to negative melting temperatures is not physical.

Curvature depresses the equilibrium melting temperature of solid convex into liquid. Here $\mathcal{K}$ is the sum of principal curvatures, equal to twice a common convention for mean curvature, and $T_m$ is absolute temperature. The coefficient uses solid-liquid surface energy, mass density and latent heat. This stabilizes fine corrugations of a solidification front.