Maximum superheating and undercooling: Systematics, molecular dynamics simulations, and dynamic experiments

Abstract

The maximum superheating and undercooling achievable at various heating (or cooling) rates were investigated based on classical nucleation theory and undercooling experiments, molecular dynamics (MD) simulations, and dynamic experiments. The highest (or lowest) temperature ${T}_{c}$ achievable in a superheated solid (or an undercooled liquid) depends on a dimensionless nucleation barrier parameter $\ensuremath{\beta}$ and the heating (or cooling) rate Q. $\ensuremath{\beta}$ depends on the material: $\ensuremath{\beta}\ensuremath{\equiv}16\ensuremath{\pi}{\ensuremath{\gamma}}_{\mathrm{sl}}^{3}{/(3\mathrm{kT}}_{m}\ensuremath{\Delta}{H}_{m}^{2})$ where ${\ensuremath{\gamma}}_{\mathrm{sl}}$ is the solid-liquid interfacial energy, $\ensuremath{\Delta}{H}_{m}$ the heat of fusion, ${T}_{m}$ the melting temperature, and k Boltzmann's constant. The systematics of maximum superheating and undercooling were established phenomenologically as $\ensuremath{\beta}{=(A}_{0}\ensuremath{-}b{\mathrm{log}}_{10}Q){\ensuremath{\theta}}_{c}(1\ensuremath{-}{\ensuremath{\theta}}_{c}{)}^{2}$ where ${\ensuremath{\theta}}_{c}{=T}_{c}{/T}_{m},$ ${A}_{0}=59.4,$ $b=2.33,$ and Q is normalized by 1 K/s. For a number of elements and compounds, $\ensuremath{\beta}$ varies in the range 0.2--8.2, corresponding to maximum superheating ${\ensuremath{\theta}}_{c}$ of 1.06--1.35 and 1.08--1.43 at $Q\ensuremath{\sim}1$ and ${10}^{12}\mathrm{K}/\mathrm{s},$ respectively. Such systematics predict that a liquid with certain $\ensuremath{\beta}$ cannot crystallize at cooling rates higher than a critical value and that the smallest ${\ensuremath{\theta}}_{c}$ achievable is 1/3. MD simulations $(Q\ensuremath{\sim}{10}^{12}\mathrm{K}/\mathrm{s})$ at ambient and high pressures were conducted on close-packed bulk metals with Sutton-Chen many-body potentials. The maximum superheating and undercooling resolved from single- and two-phase simulations are consistent with the ${\ensuremath{\theta}}_{c}\ensuremath{-}\ensuremath{\beta}\ensuremath{-}Q$ systematics for the maximum superheating and undercooling. The systematics are also in accord with previous MD melting simulations on other materials (e.g., silica, Ta and $\ensuremath{\epsilon}$-Fe) described by different force fields such as Morse-stretch charge equilibrium and embedded-atom-method potentials. Thus, the ${\ensuremath{\theta}}_{c}\ensuremath{-}\ensuremath{\beta}\ensuremath{-}Q$ systematics are supported by simulations at the level of interatomic interactions. The heating rate is crucial to achieving significant superheating experimentally. We demonstrate that the amount of superheating achieved in dynamic experiments $(Q\ensuremath{\sim}{10}^{12}\mathrm{K}/\mathrm{s}),$ such as planar shock-wave loading and intense laser irradiation, agrees with the superheating systematics.