Abstract
Metastable phases—kinetically favoured structures—are ubiquitous in nature1,2. Rather than forming thermodynamically stable ground-state structures, crystals grown from high-energy precursors often initially adopt metastable structures depending on the initial conditions, such as temperature, pressure or crystal size1,3,4. As the crystals grow further, they typically undergo a series of transformations from metastable phases to lower-energy and ultimately energetically stable phases1,3,4. Metastable phases sometimes exhibit superior physicochemical properties and, hence, the discovery and synthesis of new metastable phases are promising avenues for innovations in materials science1,5. However, the search for metastable materials has mainly been heuristic, performed on the basis of experiences, intuition or even speculative predictions, namely ‘rules of thumb’. This limitation necessitates the advent of a new paradigm to discover new metastable phases based on rational design. Such a design rule is embodied in the discovery of a metastable hexagonal close-packed (hcp) palladium hydride (PdHx) synthesized in a liquid cell transmission electron microscope. The metastable hcp structure is stabilized through a unique interplay between the precursor concentrations in the solution: a sufficient supply of hydrogen (H) favours the hcp structure on the subnanometre scale, and an insufficient supply of Pd inhibits further growth and subsequent transition towards the thermodynamically stable face-centred cubic structure. These findings provide thermodynamic insights into metastability engineering strategies that can be deployed to discover new metastable phases.
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Data availability
The data that support the findings of this study are available from the corresponding author upon request.
Code availability
MC simulation code and data for the nanoparticle stability analysis are available at GitHub repository https://github.com/scychon/HCP-PdH. Atomic electron tomography code and data are available at http://mdail.kaist.ac.kr/HCP-PdH.
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Acknowledgements
This research was supported by the National Research Foundation (grant nos. 2018M3D1A1058793, 2015M1A2A2074688, 2018M1A2A2061975, 2021M3H4A1A02042948, 2019R1F1A1058236, 2020R1C1C1006239, 2020R1F1A1060331 and 2019M3E6A1064877), the Korea Institute of Science and Technology (grant no. 2E30201), the KAIST-funded Global Singularity Research Program (M3I3) and the Institute for Basic Science (grant no. IBS-R006-D1).
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J.H., J.-H.B., S.J.Y. and D.W.C. conceived the research. J.H. and J.-H.B. designed and performed the experiments and analysed the results. H.J. and Y.Y. conducted AET. H.-Y.P. and S.L. contributed to the synthesis and analysis of nanoparticles. S.J.H., H.C., B.H. and Y.-S.L. carried out the DFT calculations and analysis. C.Y.S. performed the MC calculations and analysis. M.K.C., Juyoung K. and H.B. performed the TEM and EELS acquisition and analysis, whereas S.-C.K. performed the Rietveld refinement analysis. Joodeok K., Y.S., T.H. and J.P. interpreted the dynamics of the nanoparticles in liquids. K.L. and S.H.K. analysed the in situ TEM images. H.J., J.-Y.S., H.-K.R., K.H.L., H.-S.K., K.Y.C., C.W.Y., J.-P.A., G.H.K. and S.J. discussed and commented on the results. J.H., J.-H.B., H.J., C.Y.S., Y.Y., Y.-S.L., S.J.Y. and D.W.C. wrote the manuscript. C.Y.S., Y.Y., Y.-S.L., S.J.Y. and D.W.C. supervised the project. All authors approved the final version of the manuscript for submission.
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Extended data figures and tables
Extended Data Fig. 1 Estimation of the lattice parameters of hcp PdHx and chemical analysis of hcp particles.
a, The DFT-optimized and experimental lattice parameters of fcc PdHx are used to improve the prediction of the lattice parameters of hitherto unknown hcp PdHx. 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 GLC55,56. 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.
Extended Data Fig. 2 H occupancy in finite-sized PdHx nanoparticles with different crystal packing.
a–f, Partitioning of H atoms in PdH nanoparticles with different particle sizes and crystal packing with these H atoms occupying various Pd interstitial sites in nanoparticles with high H content (x = 1) (a–c) and low H content (x = 0.2) (d–f), respectively. The H sites are categorized by the number of coordinating Pd atoms, where surface (a, d), tetrahedral (b, e), or highly occupied (trigonal bipyramidal/octahedral) (c, f) represent 0–3, 4, or 5–6 Pd atoms within the coordinating distance from the H atom, respectively. g, h, Representative coordination structure of PdH showing H atoms in the octahedral (white) and tetrahedral (green) interstitial sites formed by fcc (g) and hcp (h) crystal packing. Pd atoms are shown as large spheres, and the colors represent different Pd layers. The 1-4-layer overlap (ABCA’) in the fcc Pd structure provides extra stabilization for octahedral H atoms, while the 1-3-layer overlap (ABA’) in the hcp Pd structure provides extra stabilization to tetrahedral (T) and trigonal bipyramidal (TB) H atoms, resulting in distinct H atom occupancy, especially in small nanoparticles. At a diameter of 1.2 nm, almost half of the H atoms reside on the surface, regardless of the crystal packing.
Extended Data Fig. 3 Concentration of radiolysis products as a function of time and EDR.
a, Evolution over time of the concentrations of eh−, H•, and H2 under low EDR. b, Steady-state concentrations of eh−, H•, and H2 under low, medium, and high EDRs. The concentrations were calculated assuming uniform irradiation of the neat water using a publicly available code9,58. In a, the steady state developed rapidly, and the concentration remained the same after 1 ms. The steady-state values were used to draw b. The uniform irradiation condition does not ideally describe the experimental conditions; nonetheless, the concentrations of eh−, H•, and H2 are expected to increase with increasing EDR. c, Parameters used for electron dose rate calculation. Screen current, beam radius, and magnification used in three different conditions and corresponding EDRs. These parameters set at the described magnification were measured in TEM user interface software and used to calculate the EDR values. Fluctuations in the screen current are shown on a percentage scale and are almost negligible.
Extended Data Fig. 4 Formation of nanoparticles around a hydrogen bubble evolved in GLC and in a batch reactor outside TEM.
a, Sequence of TEM images acquired by in situ analysis, showing the nucleation and subsequent growth and dissolution of nanoparticles on the surface of a bubble, recorded under high EDR. These particles are thought to be generated via the condensation of Pd ions around a bubble as gas molecules push other chemicals away. b, In situ HR-TEM images and corresponding FFTs of the nanoparticles formed on the surface of the bubble in a. Both fcc and hcp nanoparticles were generated. Notably, the interplanar distances of the fcc particles are 3–4% larger on average than those of pure fcc Pd, indicating the formation of fcc PdHx particles. The production of fcc particles around hydrogen bubbles (which form when the radiolysis products exceed their critical concentration9) is another piece of evidence for the key role of H in the formation of the hcp structure. These bubbles remove supersaturated H, resulting in a lower H/Pd condition favoring the formation of fcc PdHx around the bubble. c, Ex situ HR-TEM images of Pd nanoparticles grown on the surface of carbon black in a batch reactor that utilizes an electron beam with a dose rate of 1.9 × 10−3 e− Å−2 s−1, showing only fcc particles. d, Le Bail fitting results for the XRD pattern of the Pd/C synthesized in the batch reactor. The asterisks and the “v” mark on the peaks correspond to internal standards of Si powder (NIST SRM 640e) and graphite (PDF# 04-006-5764), respectively. e, Schematic illustration of electron-beam-assisted Pd nanoparticle synthesis using a large-scale batch reactor. Scale bars, 20 nm (a), 5 nm (b), and 2 nm (c). ZA, zone axis.
Extended Data Fig. 5 Calculated and experimental Vf.u. of hcp and fcc PdHx.
a, b, Comparison of Vf.u. of the nanoparticles and bulk phase for hcp (a) and fcc (b) PdHx. DFT-calculated and experimental volumes were used for bulk hcp PdHx and fcc PdHx, respectively. In the DFT result, H atoms are placed at the tetrahedral sites after all the available octahedral sites are filled for x greater than 1. The H content x in the nanoparticles, which is unknown, is deduced from the volume of the corresponding structure in bulk. A linear volume change with respect to x is assumed for the interpolated x values. The Vf.u. of both hcp and fcc nanoparticles increased with increasing EDR owing to the corresponding increase in H concentration in the solution. Error bars represent standard deviations. c, Total number of particles used for deriving Vf.u..
Extended Data Fig. 6 Average size and distribution of particles.
a, b, Average size of hcp (a) and fcc (b) PdHx nanoparticles in GLC with respect to EDR and Pd concentration. c, d, Average size of hcp (c) and fcc (d) PdHx nanoparticles in SLC in static or flow mode with respect to EDR at a fixed Pd concentration (3.67 mM). Error bars represent standard deviations. e, Size difference between hcp and fcc particles (ΔDhcp-fcc) formed in conditions where both phases were observed. The average diameter of hcp particles subtracted from that of fcc particles is plotted as a function of Pd concentration, EDR, and liquid cell system. No clear trend was observed, possibly because of the complexity of the radiolysis process. Not only the average particle size and its distribution but also the total number of particles depend strongly on both the Pd and hydrated electron concentrations. These factors, along with other radiolysis-driven conditions, including hydrogen ion/radical concentration and pH, significantly influence the nucleation and growth rate of PdHx nanoparticles, which in turn determines the size distribution of the particles according to classical nucleation theory59. Furthermore, the difference in irradiation time for each EDR condition as well as the limited supply of Pd in GLC could affect the particle size and the total number of nanoparticles. Hence, it is difficult to achieve a comprehensive understanding of the size of the particles produced in the liquid cells. No systematic change was observed in the particle size of either hcp or fcc particles (a, b) or their size difference (e) with respect to Pd concentration and EDR. The number of datasets in the case of SLC (c, d) was not enough to find a reliable trend. f–q, Distribution of Vf.u. and particle diameter of hcp (f–k) and fcc (l–q) PdHx nanoparticles formed in GLC and SLC as a function of Pd solution concentration: 3.67 (f, l), 10 (g, m), 18 (h, n), 36.7 (i, o), and 73 mM (j, p) in GLC and 3.67 mM (k, q) in SLC depending on EDR. Conditions where either of hcp phase or fcc phase particles were barely observed were omitted. Vf.u. and particle diameter show no correlation with any of the three factors, EDR, Pd concentration, and liquid flow.
Extended Data Fig. 7 Energy of the PdH slab growth.
a, b, Energy required to symmetrically add Pd (a) or H (b) atomic layers on top of the (0001) hcp PdH or (111) fcc PdH slab, estimated from DFT calculations. c, Illustration of the symmetric addition of Pd and H layers, with Pd and H atoms drawn in gray and blue, respectively. The energies are defined as ΔEPd(N) = 1/2×((E(PdNHN−1)−E(PdN−2HN−1)−2×E(fcc Pd)) for the addition of N Pd atoms in a and ΔEH(N) = 1/2×((E(PdNHN+1)−E(PdNHN−1)−E(H2)) for the addition of N H atoms in b. In the case of fcc and hcp Pd slabs, the energy for Pd addition is simply expressed as ΔEPd(N) = E(PdN)−E(PdN−1)−E(fcc Pd); for fcc Pd, ΔEPd(N) approaches zero, whereas for hcp Pd, it approaches the energy difference between bulk hcp Pd and fcc Pd, which indicates that convergence has been achieved. Although ΔEPd(N) for hcp PdH and hcp Pd are similar, ΔEPd(N) for fcc PdH is higher than that for fcc Pd and even than that for hcp PdH.
Extended Data Fig. 8 Annealing a hcp PdHx nanoparticle.
a, Ex situ HR-TEM images and corresponding FFTs of a nanoparticle as synthesized at room temperature (RT) and after being annealed at 500 °C for 2 h. The hcp PdHx nanoparticle maintained its crystal structure and interplanar distances even after heat treatment. Images were acquired with two different zone axes for a single particle to confirm the hcp structure. b, Tilting a particle initially aligned along the [\overline{2}110] axis by 30° around an axis along the [0002] direction reoriented it to alignment along the [0\overline{1}10] axis, as expected in the Kikuchi pattern of hcp with c/a = 1.65. Scale bar, 2 nm. ZA, zone axis.
Extended Data Fig. 9 Detailed atomic structure and local H concentration map of a PdHx nanoparticle obtained in the GLC, showing large local fluctuations.
a, Layer-by-layer representation of the traced atomic coordinates and fitted hcp positions for two major domains of the PdHx nanoparticle shown in Fig. 4. The atoms belonging to two major domains are shown in orange and green. Each domain was separately fitted with a hcp structure, and black dots represent atoms fitted to the hcp positions. Gray dots represent the atomic positions not assigned to any domain. The layers were sliced from the top of the nanoparticle along the hexagonal c axis and plotted in vertical order starting from the top left panel. b, Layer-by-layer representation of the local H concentration map calculated from MC simulations using Pd coordinates constructed from the AET results, where the layers are ordered corresponding to a. The local fluctuation of H correlated with the large fluctuation in lattice constants (0.1–0.2 Å) observed in the statistical ex situ analysis of hcp particles (Fig. 3 and Extended Data Figs. 5a and 6f–k) as well as in situ analysis of particle growth, showing fluctuations in the d-spacing during particle growth (Fig. 1c–d). These local fluctuations might stem from the nonuniform H distribution in the liquid owing to the stochastic collisions of incident electrons and water molecules. A high H molar concentration appears near the Pd atoms with a large local lattice constant, where the H concentration reaches up to 150% of the Pd concentration. Approximately 20% of the total H atoms are found to occupy the surface region. The lower spatial H concentration marked at the surface region is due to the difference in accessible free volume per Pd atom, where surface Pd atoms have a larger Voronoi volume than the inner Pd atoms owing to less overlap with other Pd atoms. Scale bar, 1 nm.
Extended Data Fig. 10 Evolution of hcp PdHx nanoparticles in the early growth stage and multistep crystallization process.
a–d, Snapshots and corresponding FFTs from Supplementary Video 1 and 2 showing the early stages of the growth of particles 1 (a) and 2 (c) in Fig. 1a–d, along with b and d, their respective size evolutions. e, Snapshots and corresponding FFTs from Supplementary Video 4 showing the growth of another hcp PdHx particle formed under the same conditions as those of particles 1 and 2. f, Size evolution of the particle in e. g, Plot of interplanar distances of five low-index planes of the particle in e as a function of time. The zone axis patterns show that the particle had a hcp structure immediately after coalescence, that is, within approximately one second of nucleation at most. All images were obtained in situ. Scale bar, 2 nm. ZA, zone axis.
Extended Data Fig. 11 Vibrational characteristics of PdH from DFT calculations.
a, b, Phonon dispersion curves of hcp PdH, in which H is located at the ideal octahedral position (a) and H is displaced by 0.24 Å from the ideal position along the c axis (b). The corresponding atomic models are shown below the curves. Pd and H atoms are drawn in gray and blue, respectively. Imaginary phonon modes were found when H was positioned at the ideal octahedral site. One of those modes indicates the displacement of H along the c axis, with this rearrangement removing the imaginary modes, as shown in b. c, d, Energy landscape (ΔE) values around the octahedral position as calculated by displacing a single H atom from the center of the octahedron made by the six nearest-neighboring Pd atoms in the 48-atom supercell (2 × 2 × 3 hexagonal cell) of hcp PdH (c) and fcc PdH (d). The displacement toward the face in c is similar to the changes shown in a and b, but the instability is not captured. H atoms may adopt the ideal octahedral position at room temperature instead of collectively moving to the lower symmetry structure because of the small energy difference (∼1 meV/atom) between the two structures a and b. The energy variation in fcc PdH in d is more isotropic and lower in magnitude for the same degree of displacement than that in hcp PdH. This result agrees with the higher phonon frequencies of hcp PdH in this study compared with those of fcc PdH54.
Supplementary information
Supplementary Video 1
Particles grown by monomer attachment. TEM video of hcp PdHx nanoparticles growing in a GLC with 3.67 mM Pd solution. DP analysis shows the particle has hcp structure. Real-time speed was set as the standard speed (×1). The video starts at the onset of the electron beam irradiation of the liquid.
Supplementary Video 2
Particles grown by coalescence. TEM video of hcp PdHx nanoparticles growing in a GLC with 3.67 mM Pd solution. DP analysis conducted after coalescence shows the particle has hcp structure. Real-time speed was set as the standard speed (×1).
41586_2021_4391_MOESM3_ESM.mov
Supplementary Video 3 A particle grown without square fringes around it. TEM video of hcp PdHx nanoparticles growing in a GLC with 18 mM Pd solution. Square fringes are not observed throughout the whole growth process around the particle marked with a yellow arrow, and it exhibits hcp structure at the end of the video. Fringes that appeared over the area corresponded to the crystal lattice of hcp PdHx, not NaCl. The playback speed is three times as fast as the real-time speed (×3).
Supplementary Video 4
The amorphous phase at an early stage. TEM video of hcp PdHx nanoparticles growing in a GLC with 3.67 mM Pd solution. No fringes were observed during the early stage of the particle growth. The playback speed is the real-time speed.
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Hong, J., Bae, JH., Jo, H. et al. Metastable hexagonal close-packed palladium hydride in liquid cell TEM. Nature 603, 631–636 (2022). https://doi.org/10.1038/s41586-021-04391-5
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DOI: https://doi.org/10.1038/s41586-021-04391-5
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