Crystallisation kinetics of supercooled liquid palladium
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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 $700$--$1150~\mathrm{K}$ ($0.38$--$0.65 T_{\mathrm{m}}$) 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 $467(6)~\mathrm{meV/atom}$, consistent with available data for supercooled liquid metals. The steady-state homogeneous nucleation rate exhibits a maximum of approximately $4 \times 10^{35}~\mathrm{m^{-3} s^{-1}}$ near $0.5 T_{\mathrm{m}}$. Crystal growth occurs at velocities of the order of metres 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 $0.5 T_{\mathrm{m}}$ and $100~\mathrm{ps}$, corresponding to a critical cooling rate for vitrification on the order of $10^{13}~\mathrm{K s^{-1}}.$ 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 $5 \times 10^{11}~\mathrm{K s^{-1}}.$ These results indicate that homogeneous, rather than heterogeneous, nucleation governs the achievable supercooling in the experimentally studied films.
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