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

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 β and the heating (or cooling) rate Q. β depends on the material: [formula presented] where γ_sl is the solid-liquid interfacial energy, ΔH_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 β=(A₀−b log₁₀Q)θ_c(1−θ_c)₂ where θ_c=T_c/T_m, A₀=59.4, b=2.33, and Q is normalized by 1 K/s. For a number of elements and compounds, β varies in the range 0.2–8.2, corresponding to maximum superheating θ_c of 1.06–1.35 and 1.08–1.43 at Q∼1 and 10¹² K/s, respectively. Such systematics predict that a liquid with certain β cannot crystallize at cooling rates higher than a critical value and that the smallest θ_c achievable is 1/3. MD simulations (Q∼10¹² K/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 θc−β−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 ε-Fe) described by different force fields such as Morse-stretch charge equilibrium and embedded-atom-method potentials. Thus, the θ_c−β−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∼10¹² K/s), such as planar shock-wave loading and intense laser irradiation, agrees with the superheating systematics.