Extended Data Fig. 1: Estimation of the lattice parameters of hcp PdH_x and chemical analysis of hcp particles.

a, The DFT-optimized and experimental lattice parameters of fcc PdH_x are used to improve the prediction of the lattice parameters of hitherto unknown hcp PdH_x. The lattice parameter of fcc Pd at 300 K is well-known⁵², but the lattice parameter of stoichiometric fcc PdH at 300 K is not known. Hence, the lattice parameter of PdH at 77 K reported by Schirber et al.⁵³ was used, and then, the thermal expansion discussed by Errea et al.⁵⁴ was applied. As summarized in the table, the experimental lattice parameters at 300 K were found to be slightly larger than the DFT-optimized values. The estimated lattice parameters of the hcp structures were obtained by multiplying the DFT values by the ratio a (300 K, exp)/a (DFT) for the respective compositions in the fcc structure. b, Ex situ HAADF-STEM image of hcp nanoparticles, marked with a yellow circle where the EDS spectrum of a hcp particle in c was acquired (same area where the EDS maps in Fig. 1h were obtained). Scale bar, 20 nm. c, EDS spectra of one of the nanoparticles (red) and a background area (black). While some residues of the precursor solution and contamination are present in the sample, the difference between the spectra of the particle and background shows that the particle consists solely of Pd. The magnified spectra (left) within the range of the full spectrum (right) denoted by the green dash-dotted box indicate the absence of boron, hence excluding the possibility that Pd–B formed in the GLC^55,56. d, EEL spectra acquired from a background Si₃N₄ window. While the black dots and red line show the raw data and fitted background, respectively, the green lines represent the background-removed EEL spectrum (top box) and its denoised version (bottom box). The SLC was used instead of the GLC to prevent overlap between the plasmon peaks of Pd and graphene⁵⁷. The absence of a peak at approximately 5.9 eV indicates that the peak that appeared in the hcp particle originated from the particle itself.