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

TL;DR

This study probes ultrafast heat transfer and nonequilibrium lattice dynamics in single Pd nanocrystals using optical laser pumping and X-ray free-electron laser probing of the 111 Bragg peak. A combination of 2D Bragg-peak analysis, incoherent imaging, and a 1D forward diffraction model, complemented by 1D TTM simulations, reveals fluence-dependent heterogeneous heating that drives a propagating strain boundary at the speed of sound and transient peak splitting. Pd-specific properties, including higher electronic specific heat and electron-phonon coupling relative to Au, yield pronounced inhomogeneous heating and robust strain patterns on ~ps–tens of ps timescales. The work demonstrates a direct, imageable link between hot-electron transport and nanoscale lattice strain, with implications for predicting reaction rates and mitigating thermal degradation in Pd-based photo-catalysis and related technologies.

Abstract

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.

Figures (5)

• Figure 1: Experimental ultrafast pump-probe X-ray diffraction setup in horizontal scattering geometry.a The samples are pumped using an 800 nm optical laser, followed by an X-ray probe with a variable delay time. An isolated $111$ Bragg peak, corresponding to a single Pd nanoparticle (green dashed circle), was measured using the adaptive gain integrating pixel detector (AGIPD) positioned 4 m from the sample at $2\theta$ = 35.8 °. White arrows indicate the $Q_x$ and $Q_y$ directions in reciprocal space. b SEM image of octahedral-shaped Pd nanocrystals coated with $\approx 10$ nm of $\mathrm{TiO_2}$ for stability. The lighter, triangle-shaped profiles show the Pd particle facets, surrounded by the darker $\mathrm{TiO_2}$ coating. These coated nanoparticles are later fixed on a Si substrate using tetraethyl orthosilicate (TEOS), which is not shown.
• Figure 2: Evolution of the $111$ Bragg peak intensity on a linear scale for crystal A at various delay times and laser fluences. Rows a - d correspond to sequential delay measurements using different fluences. The evolution of crystals B and C is shown in Supplementary Figs. \ref{['supp-fig:Bragg_peaks_B']} - \ref{['supp-fig:Bragg_peaks_C-2']}.
• Figure 3: Summary of the changes to the Gaussian-fitted Bragg peaks along the horizontal $2\theta$ direction, $Q_x$, as a function of laser fluence and delay time.a Fitted parameters for various laser fluences for Crystal A. (i) Fitted position of the Bragg peak along $Q_x$. The oscillations were fitted with Eq. \ref{['supp-eq:peak_position_fitting']} for all fluences except for $\mathrm{230\ mJ/cm^2}$ due to a lack of signal. (ii) Fitted FWHM of the Bragg peak along $Q_x$. The oscillations were fitted with Eq. \ref{['supp-eq:peak_FWHM_fitting']}. The error of the Gaussian fits is shown in Supplementary Fig. \ref{['supp-fig:Crystal_A_chi2_error']}. b Fitted parameters for a laser fluence of $\mathrm{57\ mJ/cm^2}$ on all measured crystals. c Fitted parameters for a laser fluence of $\mathrm{110\ mJ/cm^2}$ on all measured crystals. Crystal C-1 and C-2 are two successive measurements on the same crystal. The error bars reflect two standard deviations of repeated measurements at negative delay times. Oscillation periods are shown by the horizontal bars in each panel. The error of the Gaussian fits is shown in Supplementary Fig. \ref{['supp-fig:Fluence_chi2_error']} for b and c. The equivalent of this figure in the $Q_y$ direction is Supplementary Fig. \ref{['supp-fig:Bragg_peak_COM_FWHM_y']}.
• Figure 4: Real-space 2D model of crystal A in the laboratory frame up to 50 ps delay time at a $\mathrm{57\ mJ/cm^2}$, b $\mathrm{110\ mJ/cm^2}$ and c $\mathrm{170\ mJ/cm^2}$. For each subfigure, (i) the experimental Bragg peak, (ii) the model Bragg peak, (iii) the real space model displacement, $\mathbf{u_{111}}$, and (iv) the real space model strain, $\varepsilon_{111}$, are presented as rows. (i) and (ii) refer to the bottom left colour bar, (iii) refers to the bottom middle colour bar and (iv) refers to the bottom right bar. We note that $\mathbf{u_{111}}$ and $\varepsilon_{111}$ also contain the homogeneous displacement and strain that result from the Bragg peak shifts relative to negative delay times. The experimental and model Bragg peaks are both normalised for ease of comparison. The model parameters are shown in Fig. \ref{['main2:fig:Strain_disp_values']}. The centre of mass parameters are shown in Supplementary Fig. \ref{['supp-fig:Model_parameters']}c and d. The error associated with the model is shown in Supplementary Fig. \ref{['supp-fig:Model_error']}.
• Figure 5: The displacement, $\mathbf{u_{111}}$ and strain, $\mathbf{\varepsilon}_{111}$ values at different laser fluences extracted from the 2D model in Fig. \ref{['main2:fig:Model']}. The maximum and minimum $\mathbf{u_{111}}$ and $\mathbf{\varepsilon}_{111}$ are displayed in a and b, respectively. The average and standard deviations of $\mathbf{u_{111}}$ and $\mathbf{\varepsilon}_{111}$ are shown in Supplementary Fig. \ref{['supp-fig:Strain_disp_values_extra']}. The main model variables in Eq. \ref{['main2:eq:psi']}: c wave peak position, $x_0$; d positive slope, $s_1$, leading to $x_0$, and negative slope, $s_2$, descending from $x_0$. The dashed lines in c show the speed of the boundary propagation.