Homogeneous Nucleation Catastrophe as a Kinetic Stability Limit for Superheated Crystal

Homogeneous nucleation kinetics for melting in superheated crystals is analyzed in order to derive a kinetic stability limit for the crystal lattice above its equilibrium melting point $\left(T_m\right)$. It is found that at a critical temperature ( $T_m^K$, which is about ${1.2T}_m$ for various elemental metals) a massive homogeneous nucleation of melting occurs in the superheated crystal. Such a homogeneous nucleation catastrophe, which occurs before other proposed (rigidity, volume, and entropy) catastrophes can intervene, provides us with a kinetic stability limit for superheated crystals.