= Solidification attachment mobility
{title2=$U=\mathcal M(T_{\rm eq}-T_i)$}
The attachment mobility $\mathcal M>0$ is the coefficient converting interfacial undercooling into a <solidification> speed. In the linear isotropic law, $U=\mathcal M(T_{\rm eq}-T_i)$, and capillarity makes $T_{\rm eq}=T_m-\gamma_T\mathcal K$. Thus $T_i=T_m-U/\mathcal M-\gamma_T\mathcal K$. This kinetic coefficient refers to a moving <phase boundary>, rather than an order-parameter relaxation coefficient. The <Gibbs--Thomson relation> determines $\gamma_T=T_m\gamma/(\rho L)$ for isotropic <solid-liquid surface energy> $\gamma$.
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