Crystallisation Kinetics of Supercooled Liquid Palladium

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Abstract
In this study, we employ classical molecular dynamics (MD) simulations to investigate the crystallisation kinetics of supercooled liquid palladium and relate the results to time-resolved X-ray diffraction measurements on rapidly quenched Pd thin films. Crystal nucleation and growth rates are determined over the temperature range 700–1150 K (0.38–0.65 Tm) by analysing the evolution of the microstructure during the liquid-to-crystal transition. The self-diffusion coefficient of Pd, obtained from the atomic mean-squared displacement, follows Arrhenius behaviour over the investigated temperature range, with an activation energy of 467(6) meV/atom, consistent with available data for supercooled liquid metals. The steady-state homogeneous nucleation rate exhibits a maximum of approximately 4×10^35 m^-3 s^-1 near 0.5 Tm. Crystal growth occurs at velocities of the order of meters per second, with a temperature dependence consistent with diffusion-limited Wilson–Frenkel kinetics rather than the collision-limited regime. Based on multiple statistically independent simulations, a time–temperature–transformation (TTT) diagram for crystallisation onset is constructed. The TTT curve exhibits a nose near 0.5 Tm and 100 ps, corresponding to a critical cooling rate for vitrification on the order of 10^13 K/s. The simulations reproduce the crystallisation onset time and temperature observed in time-resolved X-ray diffraction experiments on optically molten Pd thin films quenched at 5×10^11 K/s. These results indicate that homogeneous, rather than heterogeneous, nucleation governs the achievable supercooling in the experimentally studied films.