Ultrafast heat transfer in single palladium nanocrystals seen with an X-ray free-electron laser

We report transient highly strained structural states in individual palladium (Pd) nanocrystals, electronically heated using an optical laser, which precede their uniform thermal expansion. Using an X-ray free-electron laser probe, the evolution of individual 111 Bragg peaks is measured as a function of delay time at various laser fluences. Above a laser fluence threshold at a sufficient pump-probe delay, the Bragg peak splits into multiple peaks, indicating heterogeneous strain, before returning to a single peak, corresponding to even heat distribution throughout the lattice expanded crystal. Our findings are supported by a lattice displacement and strain model of a single nanocrystal at different delay times, which agrees with the experimental data. Our observations have implications for understanding femtosecond laser interactions with metals and the potential photo-catalytic performance of Pd.

💡 Research Summary

In this work the authors combine an 800 nm optical pump with femtosecond X‑ray free‑electron laser (XFEL) probing to monitor the structural response of individual palladium (Pd) nanocrystals on picosecond timescales. Octahedral Pd particles (≈50–100 nm) coated with ~10 nm TiO₂ were deposited on a Si substrate. Pump fluences ranging from 57 to 230 mJ cm⁻² were applied, and the 111 Bragg peak of each particle was recorded as a function of pump‑probe delay (0–300 ps) using a 2‑meter‑distance detector.

At the lowest fluence (57 mJ cm⁻²) the Bragg peak exhibits a modest shift in the horizontal (Qₓ) direction, reflecting a homogeneous lattice expansion driven by electron‑phonon coupling, while the peak shape remains essentially unchanged. When the fluence exceeds ~110 mJ cm⁻², a clear splitting of the 111 peak appears around 30 ps delay, indicating the simultaneous presence of compressed and expanded regions within the same crystal. This heterogeneous strain persists for roughly 20 ps and then collapses, giving way to a single, broadened peak that gradually returns to a uniform expansion state. At higher fluences (170–230 mJ cm⁻²) the splitting becomes more pronounced, the peak intensity drops sharply, and the crystal undergoes a measurable out‑of‑plane rotation of up to ~0.06°, inferred from vertical (Qᵧ) shifts. The intensity loss is attributed both to rotation out of the Bragg condition and to the reduced coherent scattering caused by strain gradients.

The authors fit each 2‑D diffraction pattern with a single Gaussian to extract peak centre positions and full‑width‑at‑half‑maximum (FWHM) along Qₓ. The centre motion provides the average lattice strain, while the FWHM tracks heterogeneous strain. Oscillations of the centre with a period of ~120 ps are observed for all fluences, corresponding to the lowest‑frequency vibrational mode of the nanocrystal. Simultaneously, the FWHM oscillates with a period of ~60 ps—exactly half the vibrational period—consistent with an acoustic wave reflecting back and forth, periodically maximising strain gradients.

To interpret the transient peak splitting, the authors employ a 1‑D forward model inspired by Bragg coherent diffraction imaging (BCDI). The model treats the crystal as a rectangular object with a single internal boundary at x₀. In the region x ≤ x₀ the phase ramps up with slope s₁ (positive displacement), while for x > x₀ it ramps down with slope s₂ (negative displacement). These three parameters (x₀, s₁, s₂) reproduce the observed double‑peak structure and the broadened FWHM without invoking full 3‑D phase retrieval, which was hampered by low signal‑to‑noise. The fitted phase gradients translate directly into local lattice displacement u₁₁₁ and strain ε₁₁₁ along the scattering vector. The model shows that the laser‑generated hot electrons penetrate only a few nanometres from the surface, creating a highly non‑uniform electronic temperature profile. Electron‑phonon coupling then transfers this energy to the lattice, producing a compressive front that propagates inward while the outer region expands, yielding the observed heterogeneous strain pattern.

Comparing Pd to previously studied Au nanocrystals, the authors note that Pd exhibits a stronger electron‑phonon coupling constant and a shorter electron mean free path, leading to more pronounced early‑time strain heterogeneity. In Au, similar pump‑probe experiments reported largely homogeneous expansion with no detectable compression. The present results therefore highlight material‑specific pathways of ultrafast heat diffusion in metallic nanostructures.

The implications are twofold. First, the work provides a direct, single‑particle view of how electronic energy is redistributed within a metal nanoparticle on sub‑100 ps timescales, bridging the gap between atomistic simulations and ensemble‑averaged measurements. Second, the transient coexistence of compressed and expanded lattice regions could modulate surface electronic states and adsorption energies, suggesting a route to enhance photocatalytic activity of Pd by exploiting the non‑thermal strain dynamics induced by femtosecond laser excitation.

Overall, the paper demonstrates that ultrafast XFEL diffraction, combined with careful Gaussian analysis and a simple yet effective forward phase model, can resolve the full temporal evolution—from initial electronic heating, through heterogeneous strain formation, to eventual uniform thermal expansion—of individual palladium nanocrystals. This methodology opens new avenues for probing and controlling heat transport, phase transitions, and catalytic behavior in nanoscale metals.