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) meV/atom, consistent with available data for supercooled liquid metals. The steady-state homogeneous nucleation rate exhibits a maximum of approximately 4 × 10³⁵ m⁻³ s⁻¹ near 0.5 T_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_m and 100 ps, corresponding to a critical cooling rate for vitrification on the order of 10¹³ 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 × 10¹¹ 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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BibTeX RIS

BibTeX

@misc{kostera2026crystallisation,
  title = {{Crystallisation kinetics of supercooled liquid palladium}},
  author = {Zuzanna Kostera and Przemyslaw Dziegielewski and Christian Bressler and Wojciech Gawelda and Konstantinos Georgarakis and Dmitry Khakhulin and Oleksii I. Liubchenko and Adam Olczak and Angel Rodriguez-Fernandez and Ryszard Sobierajski and Klaus Sokolowski-Tinten and Peihao Sun and Robert W. E. van de Kruijs and Hazem Yousef and Peter Zalden and Jerzy Antonowicz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.31399},
  eprint = {2605.31399},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.31399},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Crystallisation kinetics of supercooled liquid palladium
AU  - Zuzanna Kostera
AU  - Przemyslaw Dziegielewski
AU  - Christian Bressler
AU  - Wojciech Gawelda
AU  - Konstantinos Georgarakis
AU  - Dmitry Khakhulin
AU  - Oleksii I. Liubchenko
AU  - Adam Olczak
AU  - Angel Rodriguez-Fernandez
AU  - Ryszard Sobierajski
AU  - Klaus Sokolowski-Tinten
AU  - Peihao Sun
AU  - Robert W. E. van de Kruijs
AU  - Hazem Yousef
AU  - Peter Zalden
AU  - Jerzy Antonowicz
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2605.31399
UR  - https://arxiv.org/abs/2605.31399
AB  - 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) 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 T_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_m and 100 ps, corresponding to a critical cooling rate for vitrification on the order of 10^13 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 × 10^11 K s^−1. These results indicate that homogeneous, rather than heterogeneous, nucleation governs the achievable supercooling in the experimentally studied films.
ER  -

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