Crystallisation kinetics of supercooled liquid palladium

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 $700$--$1150~\mathrm{K}$ ($0.38$--$0.65 T_{\mathrm{m}}$) 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.