Superheating of Crystalline Solids: Theory, Experiment, Simulation and Applications to Static and Dynamic High-pressure Melting

Systematics of superheating (Θ =Δ T/T_m, where Δ T is the amount of superheating and T_m melting temperature) of crystalline solids as a function of heating rate (Q) are established by defining a dimensionless energy barrier for nucleation, β=16π γ_sl³/(3kT_mΔ H_m²) where γ_sl is the solid-liquid interfacial energy, Δ H_m is the heat of fusion and k Boltzmann constant. Under conditions that lead to homogeneous nucleation (e.g., ultrafast internal heating), superheating is more pronounced. Sound speed and shock temperature measurements on various materials (Fe, V, Mo, Ta, W, CsBr, KBr, SiO₂, and Mg₂SiO₄) under planar impact (Q~ 10¹² K/s) leads to superheating of Θ =0.2-0.6. Comparable superheating was achieved during intense laser irradiation (Q~ 10¹²-10¹⁵ K/s) on Al, Pb and GaAs. These observations are captured by the Θ -β-Q systematics. Homogeneous nucleation is inherent in molecular dynamics simulations of perfect bulk crystals with typical heating rates Q (~ 10¹²-10¹³ K/s) similar to those in shock wave loading and intense laser irradiation. Single-phase and two-phase simulations of melting of fcc metals (Al, Ni, Cu, Rh, Pd, Ag, Ir, Pt, and Au), a bcc metal (Ta), oxides (MgO and SiO₂) with various types of force field (FF) such as embedded atom method potential, first-principle potential and Morse-stretch charge equilibrium FF etc., have demonstrated superheating consistent with the superheating systematics. Despite of the large range of melting temperatures observed, the extrapolation of melting curves from diamond-anvil-cell experiments on V, Mo, Ta and W remain discrepant with shock wave results even when superheating and experiment uncertainties are taken into account. In the case of Fe, the discrepancy is less pronounced. This may result from a not yet explored solid-solid phase transition.