Precursor solution. The palladium precursor solution was prepared by dissolving sodium tetrachloropalladate(II) (Na2PdCl4, Aldrich) and isopropyl alcohol (Junsei) in distilled water31. The Pd concentration varied from 3.67 mM to 18 mM, but it did not affect the phase and molar volume of nucleated particles. Most experiments were performed with a 3.67 mM precursor solution. Isopropanol was used as a hydroxyl radical scavenger to minimize the probability of dissolving palladium nanoparticles. The molar concentration of isopropanol in the aqueous solution was 0.1 M9,32.
Liquid TEM cell. The graphene liquid cell (GLC) was fabricated following the previous reports8. Multilayer graphene, which was purchased from Graphene Square Incorporation, was adopted to increase durability of GLC under bombardment of electrons accelerated at a few hundred kilovolts. Silicon nitride liquid cell (SLC) experiments were conducted with a commercial in situ liquid holder, Protochips Poseidon 210, the window of which was 50 nm thick.
TEM. Electron-beam-induced PdHx nanoparticle growth in liquid was traced in real time with a Titan TEM (FEI Titan 80-300) operated at 300 kV, which was equipped with a OneView CCD camera (Gatan) and a monochromator. We used this TEM to irradiate electrons on a liquid cell to generate particles for ex situ analysis, which was conducted after fully drying the liquid, i.e. by irradiating the liquid in the GLC for ~30 min or exposing the disassembled SLC to vacuum for 48 h. HR-TEM and HR-STEM images as well as raw images for AET of the particles generated in GLC under a high electron dose rate were acquired with a double Cs-corrected Titan Themis TEM (FEI) operated at 300 kV. HR-TEM images of the particles generated at lower dose rates or in SLCs were obtained using the aforementioned Titan TEM.
Monochromated electron energy loss (EEL) spectra of the HCP particles formed inside the SLC were acquired using the Titan TEM operated at 80 kV6,33. Energy dispersive X-ray spectroscopy (EDS) analysis was conducted with a Talos TEM (FEI Talos F200X) operated at 200 kV, equipped with a Super-X EDS system that utilizes four silicon drift detectors (SDD).
XRD. X-ray diffraction (XRD) analysis was performed at room temperature in the 2θ range of 10–90° on a D8 Advance (Bruker AXS, Germany) diffractometer equipped with a LynxEye line detector using Cu-Kα radiation (λ = 1.5418 Å) at 40 kV and 40 mA and a scanning rate of 0.5 °/min with a step size of 0.02°.
In order to prove that the lattice of Pd/C was expanded relative to that of pristine Pd, an internal standard of Si powder (NIST SRM 640e) was used. The lattice parameters of Pd/C were refined with the Le Bail method34 using TOPAS software (Bruker AXS, Germany)35; the lattice parameter of Si was fixed to a = 5.431179 Å.
Lattice constant calculation. The lattice constants of the nanoparticles were calculated from the diffraction patterns of the HR-TEM and HR-STEM images of nanoparticles along the [1-21-3] and [-2110] zone axes. We used the crystallographic relationship formula of the HCP structure below to derive the lattice constants36.
![](data:image/png;base64,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)
The lattice constant a was directly calculated from the (1-100) planes, and the lattice constant c was calculated from the (1-101) planes and the aforementioned (1-100) planes for the particle along the [1-21-3] zone axis. As for the particle along the [-2110] zone axis, the lattice constants a and c were directly calculated from the (0-110) and (0002) planes, respectively. Notably, some particles had quite different lattice constants from the majority of particles. Specifically, some particles had far higher c values, while others had far lower values. These differences were attributed to the deviation in the number of H atoms residing in the particles. As the HCP palladium hydride nanoparticles formed explosively, some particles might have been formed in out-of-average surroundings, i.e., some might have been exposed to an excess of H radicals, while others might have not.
In situ d-spacing tracking. The plane index of diffraction spot, and corresponding d-spacing, acquired when the particle was aligned along the zone axis was obvious, as plane information is manifested in the zone axis pattern. When the particle was not along the zone axis, the diffraction spot of the particle was assigned to a plane index considering the continuity of fringes, and the degree of proximity between the aforementioned d-spacing value in the video and average interplanar distance measured ex situ.
Bulk scale PdHx/C preparation through e-beam irradiation. To synthesize PdHx nanoparticles via irradiation with an electron beam in a batch reactor outside TEM, 1 L of 3.67 mM Na2PdCl4 in a 0.1 M isopropyl alcohol aqueous solution was prepared. Then, carbon black was added to the reaction solution, which was homogeneously mixed under ultrasonication for 10 min at room temperature. Thereafter, the reaction vessel was placed under electron beam irradiation at a dose rate of 1.9 × 10-3 e-/Å2s for several minutes. The resulting solution was filtered with distilled water several times, and black precipitates were obtained.
Data acquisition. A tomographic tilt series of a PdHx nanoparticle was obtained using the Titan Themis TEM. In HAADF-STEM mode, 33 tilt series images of 1,024 × 1,024 pixels were obtained between -70.0° and +70.0° with a 35.50 pm pixel size. Ten images were consecutively acquired for each tilt angle with a 3 μs dwell time. A linear drift constant was estimated from consecutive images and corrected for each angle. Then, scan distortion correction was applied to correct the image distortions owing to slight misalignment between the x and y directions of the scan coil, based on a reference image of the Si (110) zone axis taken under the same measurement conditions.
Image denoising. HAADF-STEM images suffer from Poisson–Gaussian noise. The Poisson and Gaussian noise parameters were estimated from the image statistics of the ten consecutively acquired images, and a sparsity-based transform domain denoising (BM3D) was applied, as described in Refs. 10–14.21-24,37
GENFIRE reconstruction. After denoising, the projections were aligned based on the common line and center of mass methods for alignment along the tilt axis direction and perpendicular to the tilt axis direction, respectively23,24,37-39. Tomographic reconstruction was performed using GENFIRE for the aligned tilt-series images23,24,37-40 with an oversampling ratio of 4 and interpolation radius of 0.1 pixel. To improve the quality of the reconstruction, an angular refinement process was applied to minimize the discrepancy between the forward-projected projections of the reconstruction volume and the experimental projections40. The final reconstruction obtained after the refinement process showed a clear atomic-resolution internal structure.
3D identification of atomic coordinates (tracing). The 3D atomic coordinates of all atoms in the nanoparticle were determined by fitting a 3D Gaussian function on a 5 × 5 × 5 voxel volume near each local maximum. The fittings were performed in descending order from the highest intensity local maximum, and a minimum distance constraint of 2.4 Å was enforced during the process. However, owing to the atom elongation effect resulting from the missing wedge and slight imperfectness of the reconstruction, several connected intensity blobs were not properly traced owing to the failure to properly identify the local maxima. To locate the untraced atoms, the reconstruction volume was sliced along the hexagonal c axis at each atomic layer, and the local maxima in each slice were identified. Then, the same Gaussian fitting procedure was repeated using the new local maxima in descending order, still enforcing the same minimum distance constraint. After this process, a final 3D atomic model of 9,868 atoms was obtained.
Assignment of HCP lattice sites. To analyze the 3D atomic structure, proper HCP lattice sites must be assigned for each atom. To begin the assignment procedure, the HCP lattice vectors for the nanoparticle were roughly estimated from the peak positions in the 3D Fourier transformed reconstruction volume. Then, an atom closest to the mean position of the given 3D atomic coordinates was selected. The first selected atom was assigned to the origin of the HCP lattice. From the starting atom, the positions of the 12 nearest neighbor (n.n.) atoms and corresponding n.n. HCP lattice sites were calculated. At each n.n. position, a sphere was drawn with a radius of ¼ n.n. distance. If an atom was encompassed by the sphere, the atom was assigned to the lattice site corresponding to the n.n. position. This process was continued for all newly assigned HCP lattice sites and repeated until there were no newly assigned sites. Note that an atom in an HCP structure can have two different types of n.n. structure, as described in Fig. 4d. To determine which n.n. structure the starting atom belonged to, the process above was repeated twice for two different n.n. structures, and the one that resulted in a larger number of assigned HCP sites was chosen. After assigning HCP lattice sites for all available atoms, the HCP lattice vectors were fitted to minimize the error between the measured atomic positions and the corresponding lattice positions of the fitted HCP lattice. The entire process described above was continuously repeated with the newly obtained HCP lattice vectors until there the lattice vectors stopped changing.
Domain identification. For the initial trial, HCP lattice assignment and lattice parameter fitting were performed assuming that the entire nanoparticle is an HCP single crystal, resulting in initial HCP lattice vectors. However, the nanoparticle is not guaranteed to form a single crystal. Therefore, local lattice assignments and fittings described above were individually performed for all the atoms within the nanoparticle to check their n.n. ordering. For the local fitting, only the atoms within the distance of the mean of n.n. and next-nearest-neighbor (n.n.n.) distance, which was determined from the HCP fitting of the entire nanoparticle, were used. From the local fittings, the local lattice constant and n.n. structure type (Fig. 4d, named as type A or type B here) can be obtained for each atom. After the local fitting, all the atoms were assigned to the closest atomic layer perpendicular to the hexagonal c axis (Fig. 4e). Then, type-A atoms in odd-numbered layers and type-B atoms in even numbered layers were classified as ABAB stacking, and the opposite cases were classified as BABA stacking. As shown in Fig. 4e, atoms with the same stacking type form clusters.
To identify the connected clusters, we performed a local connectivity analysis. First, we selected a starting atom, around which we drew a sphere, with the mean of the n.n. and n.n.n. distance for the radius. Then, among the atoms within the sphere, we counted how many atoms share the same stacking type with the selected atom. If the number was larger than a certain threshold, the selected atom was considered to be within a connected domain, and a specific domain identifier was assigned to it. In this case, we added atoms with the same stacking type as the selected atom to the potential domain atom list, and we repeated the process for all the newly added atoms in the list. For all the atoms that fulfilled the number threshold, the same domain identifier was assigned. For atoms which could not meet the number threshold, we checked whether all of the atoms in their local sphere had the same atom type. If that was the case, we assigned the same domain identifier to the atom. Otherwise, the atom was marked as a non-domain atom (not belonging to any domain). We repeated the procedure above until there were no newly added atoms in the potential domain atom list. Finally, a collection of atoms with the same domain identifier could be identified, which formed a domain. We repeated this entire process with each other atom as a starting atom with a different domain identifier. After running the process through all available atoms, all connected domains in the nanoparticle could be identified. Individual HCP lattices could be separately assigned and fitted to each identified domain to correctly determine their lattice constants.
We tested several different number thresholds for this analysis, and using a number threshold of 7 yielded the largest number of atoms successfully assigned to HCP lattice sites after separate domain fittings. Using this threshold, we found five connected domains in the nanoparticle, which contained 3,392, 3,552, 9, 7, and 2 atoms. The remaining 2,906 atoms were not assigned to any domain. Finally, the HCP lattice constants of a = 2.9539 Å and c = 4.6692 Å were obtained by averaging each domain’s lattice constants weighted by the number of atoms.
DFT calculations. The stability of FCC PdHx and HCP PdHx was compared using density functional theory (DFT) calculations, which were carried out using the Quantum-ESPRESSO package41,42 with PBEsol43 as an exchange-correlation functional and the projector augmented wave44 pseudopotentials generated by the atomic code45. The PBEsol functional was employed because it accurately reproduces the experimental lattice parameters of PdH46, which is important in the current study. The planewave cut-off energy was set to 60 Ry. We performed phonon calculations within the density functional perturbation theory47 implemented in the Quantum-ESPRESSO package. The lattice constants of the FCC and HCP Pd and PdH crystals were varied until the optimized lattice parameters were obtained (Extended Data Table 1). The inclusion of the zero-point energy via phonon calculation (Extended Data Fig. 9) is critical for properly comparing the relative stabilities of octahedral vs. tetrahedral occupations of H atoms in Pd interstitial sites46,48.
To understand the surface effect in a PdHx nanoparticle, a 2D slab model, infinite in the a–b plane and finite along the c axis, was employed because the full description of a 3D nanoparticle is computationally demanding. To suppress the interaction between periodic images along the c axis, a vacuum region of at least 8 Å was inserted. Owing to the symmetric arrangement of the atoms, no net dipole moment developed, and the error caused by the periodic images was minimal. The energy changes upon the layer-by-layer growth of the FCC and HCP PdH slabs were compared (Extended Data Fig. 5). Alternating Pd and H layers were added, and the formation energy was calculated with respect to FCC Pd and H2.
Monte Carlo (MC) simulation using embedded atom method (EAM) potential model. The stability of bulk PdHx crystals with different crystal packing was analyzed using the classical interatomic potential for Pd–H based on the embedded atom method (EAM), which predicts the lattice constants and elastic properties of PdHx14. The total energy of the bulk PdHx crystals was calculated using the EAM potential at the DFT-optimized geometry for HCP/FCC PdHx. The DFT-optimized lattice constants were scaled to match the experiments. The H atoms were placed exactly at the octahedral (O) or tetrahedral (T) interstitial sites of the Pd atom unit cells. For the T occupation, H atoms in the equivalenced PdH crystal would fill half of all tetrahedral sites, which were modelled as zinc-blende and wurtzite structures for FCC PdH and HCP PdH, respectively.
An MC simulation of finite-sized PdH nanoparticles was performed to understand the effects of particle size and crystal packing on the relative thermodynamic stability and the internal structure of the nanoparticles. The radii of the nanoparticles were varied from 6 to 30 Å, wherein the Pd atoms were prepared with two different crystal packing (FCC/HCP). The Pd atoms in the FCC/HCP nanoparticles were positioned with ideal FCC and HCC packing using the lattice constants of FCC/HCP PdH obtained from DFT calculations (with scaling to match the experimental lattice constant). The lattice constant of partially hydrogenated PdHx was obtained by linearly scaling the lattice constants of PdH and pure Pd crystals with FCC/HCP packing. In addition, MC simulations were performed to construct a local H concentration map in the experimentally obtained HCP PdH nanoparticle, which used the 3D atomic coordinates of Pd atoms obtained from the AET experiment.
Each MC move involved the random displacement of H atoms in the fixed Pd nanocrystals. Initially, all H atoms were randomly placed inside the nanoparticles. Each new H atom position was accepted or rejected via Metropolis criteria in the NVT ensemble, where the system temperature was set at 300 K. To ensure that H atoms remained in the nanoparticle, new H positions that were not within a cut-off distance of 2.5 Å from any Pd atoms were rejected. The total energy of the system was equilibrated after a half million accepted MC moves for the smallest nanoparticles. Each nanoparticle was simulated until 5 million MC moves were accepted. The trajectory of the H atom positions was saved for every 100 successful MC moves. The total energy of the nanoparticles and the H occupancy at different interstitial sites (Fig. 2, Extended Data Figs. 2, 7b) was statistically analyzed by averaging the last 1,000 snapshots from each simulation trajectory.
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