= Nanoparticle melting-point depression
{title2=$\Delta T=2\gamma T_m/(r\Delta H_V)$}
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.
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