Nanoparticle melting-point depression ($\Delta T=2\gamma T_m/(r\Delta H_V)$)

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.