= Critical radius for a supercooled spherical seed
{title2=$a_c=\Gamma/(T_s-T_\infty)$}
The <Gibbs--Thomson relation> depresses a spherical interface's equilibrium temperature by $\Gamma/a$. For $a>a_c$, its interface is warmer than the supercooled ambient and heat loss drives growth. For $a<a_c$, its interface is colder than the ambient and heat gain drives melting. The equilibrium radius is unstable because the derivative of the quasistatic radius velocity at $a_c$ is positive.
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