The maximum superheating and undercooling achievable at various heating ͑or cooling͒ rates were investigated based on classical nucleation theory and undercooling experiments, molecular dynamics ͑MD͒ simulations, and dynamic experiments. The highest ͑or lowest͒ temperature T c achievable in a superheated solid ͑or an undercooled liquid͒ depends on a dimensionless nucleation barrier parameter ␤ and the heating ͑or cooling͒ rate Q. ␤ depends on the material: ␤ϵ16␥ sl 3 /(3kT m ⌬H m 2 ) where ␥ sl is the solid-liquid interfacial energy, ⌬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 ␤ϭ(A 0 Ϫb log 10 Q) c (1Ϫ c ) 2 where c ϭT c /T m , A 0 ϭ59.4, bϭ2.33, and Q is normalized by 1 K/s. For a number of elements and compounds, ␤ varies in the range 0.2-8.2, corresponding to maximum superheating c of 1.06 -1.35 and 1.08 -1.43 at Q ϳ1 and 10 12 K/s, respectively. Such systematics predict that a liquid with certain ␤ cannot crystallize at cooling rates higher than a critical value and that the smallest c achievable is 1/3. MD simulations (Q ϳ10 12 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 c -␤-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 ⑀-Fe͒ described by different force fields such as Morse-stretch charge equilibrium and embedded-atom-method potentials. Thus, the c -␤-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 (Qϳ10 12 K/s), such as planar shock-wave loading and intense laser irradiation, agrees with the superheating systematics.

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Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.

The ultrafast evolution of microstructure is key to understanding high-pressure and strain-rate phenomena. However, the visualization of lattice dynamics at scales commensurate with those of atomistic simulations has been challenging. Here, we report femtosecond x-ray diffraction measurements unveiling the response of copper to laser shock-compression at peak normal elastic stresses of ~73 gigapascals (GPa) and strain rates of 10(9) per second. We capture the evolution of the lattice from a one-dimensional (1D) elastic to a 3D plastically relaxed state within a few tens of picoseconds, after reaching shear stresses of 18 GPa. Our in situ high-precision measurement of material strength at spatial (<1 micrometer) and temporal (<50 picoseconds) scales provides a direct comparison with multimillion-atom molecular dynamics simulations.