Single-shot 3D coherent diffractive imaging of core-shell nanoparticles with elemental specificity

Abstract

We report 3D coherent diffractive imaging (CDI) of Au/Pd core-shell nanoparticles with 6.1 nm spatial resolution with elemental specificity. We measured single-shot diffraction patterns of the nanoparticles using intense x-ray free electron laser pulses. By exploiting the curvature of the Ewald sphere and the symmetry of the nanoparticle, we reconstructed the 3D electron density of 34 core-shell structures from these diffraction patterns. To extract 3D structural information beyond the diffraction signal, we implemented a super-resolution technique by taking advantage of CDI's quantitative reconstruction capabilities. We used high-resolution model fitting to determine the Au core size and the Pd shell thickness to be 65.0 ± 1.0 nm and 4.0 ± 0.5 nm, respectively. We also identified the 3D elemental distribution inside the nanoparticles with an accuracy of 3%. To further examine the model fitting procedure, we simulated noisy diffraction patterns from a Au/Pd core-shell model and a solid Au model and confirmed the validity of the method. We anticipate this super-resolution CDI method can be generally used for quantitative 3D imaging of symmetrical nanostructures with elemental specificity.

Figure 1

Schematic layout of the single-shot 3D diffractive imaging set-up. XFEL pulses with an energy of 6 keV and a pulse duration of 5–6 fs were focused to a 1.5 μm spot by a pair of K-B mirrors. A four-way cross slit was used to eliminate the parasitic scattering from the mirrors. Au/Pd core-shell nanoparticles with a monodisperse shape and size distribution (insets) were supported on a 100-nm-thick Si₃N₄ membrane grid and raster scanned relative to the focused beam. Each intense x-ray pulse produced a single-shot diffraction pattern, recorded by an octal multi-port charge-coupled device. A small hole was created on the Si₃N₄ membrane after a single exposure (insets).

Figure 2

Semi-automated data analysis and 3D reconstruction pipeline. (a) A large number of diffraction patterns were experimentally collected consisting of no, partial, single, and multiple hits by XFEL pulses. High-quality single-hit diffraction patterns were selected from these patterns. The different colors in the pattern are due to the difference of the read-out noise of the detector segments. (b) After background subtraction and center localization, each diffraction pattern was binned by 9 × 9 pixels to enhance the signal-to-noise ratio and the orientation of the pattern was determined. (c) By taking advantage of the curvature of the Ewald sphere and symmetry intrinsic to the nanoparticle, a single-shot diffraction pattern was used to produce a 3D Cartesian grid of the Fourier magnitudes by a gridding method. (d) The 3D phase retrieval was performed by the OSS algorithm. Among 1,000 independent reconstructions, the top 10% with the smallest R-factors were averaged to obtain a final 3D reconstruction for each single-shot diffraction pattern.

Figure 3

Quantitative analysis of the 3D reconstruction. (a) Average Phase Retrieval Transfer Function (PRTF) across all of the multiple experimental reconstructions for all 34 diffraction patterns. (b) Average Fourier shell correlation (FSC) between every pair of the 34 reconstructed nanoparticles, indicating a 3D resolution of 6.1 nm based on the criterion of FSC = 0.5. (c) Central 32-nm-thick slice of a final 3D reconstruction with an overlaid line scan plotted in (d), showing the electron density variation of the Au core and Pd shell.

Figure 4

Experimental implementation of 3D super-resolution CDI of core-shell nanoparticles. (A) and (B) The distribution of the core size and shell thickness obtained from 34 single-shot diffraction patterns. Each data point shows the mean and standard deviation of the top 10% of 1,000 independent reconstructions for a single-shot diffraction pattern. The horizontal red lines indicate the average core size and shell thickness across all 34 nanoparticles. (C) and (D) The core/shell distribution of the 34 nanoparticles, indicating the Au core size and the Pd shell thickness are 65.0 ± 1.0 nm and 4.0 ± 0.5 nm, respectively, which are beyond the diffraction signal resolution (6.1 nm).

Figure 5

Numerical simulations on 3D super-resolution CDI of nanoparticles. Noisy diffraction patterns were calculated from a core/shell model with a 65 nm Au core and a 4 nm Pd shell (a) and a solid cubic model of 73 nm Au (b). The central data in the diffraction pattern were removed to simulate a beam stop. The top 10% of 1,000 independent reconstructions were averaged and the central 20 nm sections are shown for the Au/Pd core-shell model (c) and the solid Au model (d). The small internal density variation in the reconstruction is because i) the simulated diffraction patterns were cropped to match the maximum resolution observed experimentally and ii) symmetry was enforced in assembling a 3D grid of the Fourier magnitudes. (e) Line scans through the center of the corresponding reconstructions of the Au/Pd core-shell and the solid Au model.