Nanocrystal Geometry Governs Phase Transformation Pathways in Palladium Hydride

Abstract

Pathways and structural dynamics of phase transformations impact performance of materials in energy and information storage technologies. Palladium hydride ($\mathrm{PdH}_x$) nanocrystals are an ideal model system for studying solute-induced phase transformations, where elastic energy from lattice mismatch between $α$-$\mathrm{PdH}_x$ and $β$-$\mathrm{PdH}_x$ phases is often considered a key to determining the transformation pathways. $α/β$-$\mathrm{PdH}_x$ interfacial elastic energy is affected by the confined geometry of a nanocrystal. However, how nanocrystal geometry influences phase transformation pathways is largely unknown. Using in situ liquid phase transmission electron microscopy, we directly visualize hydrogenation in Pd nanocrystals with two geometries -- a nanocube and a hexagonal nanoplate. Both follow similar sequences of an initially curved nucleus, interface flattening, and reverse-stage nucleation; however, their evolving $α/β$-$\mathrm{PdH}_x$ interfaces exhibit geometry-dependent crystallographic alignments. In nanocubes, $\{100\}$-aligned configurations conform to static elastic energy ordering, representing a pathway that maintains a local mechanical equilibrium, whereas nanoplates display both $\{110\}$- and $\{211\}$-aligned interfaces. Theoretical simulations show that geometry determines the accessibility of alternative phase transformation pathways as the system is driven far from equilibrium during hydrogenation. These findings identify geometry as a fundamental parameter for directing phase transformation pathways, offering design principles for accessing atypical configurations and improving properties of intercalation-based devices.

Figures (5)

• Figure 1: Pd nanocrystals as model systems to reveal how nanocrystal geometry governs hydrogen-induced phase transformation pathways. a, Schematic illustration of hydrogenation of Pd nanocubes (left) and nanoplates (right). b,c, Representative (HR)STEM, HRTEM, and SAED analyses of Pd nanocubes (b, along the [00-1] zone axis) and nanoplates (c, along the [11-1] zone axis) used in this study. High-resolution STEM images, obtained by enlarging boxed regions from the same nanocrystals shown in the low-magnification STEM images, resolve atomic structures. For separately selected, crystallographically equivalent nanocrystals, FFT patterns derived from HRTEM images (insets) and SAED patterns reveal consistent features: nanocubes exhibit {200} and {220} reflections, whereas nanoplates display {220} reflections together with forbidden $\frac{1}{3}${422} reflections.
• Figure 2: In situ liquid phase TEM observation of the propagation of the hydrogen-rich $\beta$-$\mathrm{PdH}_x$ phase into the hydrogen-poor $\alpha$-$\mathrm{PdH}_x$ nanocube and nanoplates during hydriding reactions. a–d, Sequential in situ HRTEM images from Movies S1–S4 (top) and corresponding amplitude-weighted d-spacing colormaps (bottom) showing the temporal evolution of $\alpha$- and $\beta$-$\mathrm{PdH}_x$ phase regions during hydrogenation of Pd Nanocube (a), Nanoplate #1 (b), Nanoplate #2 (c), and Nanoplate #3 (d). The d-spacing maps are generated using the {200} reflections for the Nanocube and the {220} reflections for Nanoplates. See Figure S7 for amplitude-weighted $\frac{1}{3}${422} d-spacing maps for Nanoplates. The hydrogen-induced phase transformation proceeds through four distinct stages: an initial nucleation event, a middle stage characterized by relatively flat $\alpha$/$\beta$-$\mathrm{PdH}_x$ interphase boundaries, a later stage resembling the reverse counterpart of the initial nucleation, and a fully transformed state. Corresponding FFT patterns of the HRTEM images are provided in Figure S8 and S9.
• Figure 3: Temporal evolution of propagating $\alpha$/$\beta$-$\mathrm{PdH}_x$ interfaces during hydrogenation of Pd nanocube and nanoplates. a–d, Contour plots showing the evolution of $\alpha$/$\beta$-$\mathrm{PdH}_x$ interfaces in the $\mathrm{PdH}_x$ nanocrystals presented in Figure 2: Nanocube (a), Nanoplate #1 (b), Nanoplate #2 (c), and Nanoplate #3 (d). The contours represent $\alpha$/$\beta$-$\mathrm{PdH}_x$ interfaces manually traced from amplitude-weighted {200}, {220}, and $\frac{1}{3}${422} d-spacing colormaps corresponding to sequential HRTEM images. Representative sequential image series used for contour extraction are provided in Figure S11–S14. The crystallographic directions indicated by schematic diagrams with arrows are assigned based on the FFT patterns in Figure S8 and S9, using the [00-1] zone axis for the nanocube and the [11-1] zone axis for the nanoplates as guidance.
• Figure 4: Free energetics and simulated hydrogenation dynamics in nanoplates. a, Helmholtz free energy as a function of the $\beta$-phase fraction ($c_\beta$) in the nanoplate. Black pentagram markers denote the transition state locations for each value of the effective chemical driving, $\Delta$$\mu$. b, Average elastic energy across simulated hydrogenation trajectories, plotted as a function of $c_\beta$. The shaded region represents the standard deviation across trajectories. Black pentagram markers correspond to the same transition-state $c_\beta$ values shown in panel a for each curve. All energies are measured in units of $k_\mathrm{B}T$, where $k_\mathrm{B}$ is the Boltzmann constant and $T$ is the simulation temperature. c, Representative snapshots from absorption trajectories in nanoplates. Each row corresponds to a single trajectory at $\Delta$$\mu$ = 0.0, 0.2, and 0.5 $k_\mathrm{B}T$ (top to bottom). Snapshots are colored in terms of the density of each phase, with blue as $\beta$-$\mathrm{PdH}_x$ and red as $\alpha$-$\mathrm{PdH}_x$. Black pentagram markers additionally indicate the snapshots corresponding to the transition state. d, Fraction of $\alpha$/$\beta$-$\mathrm{PdH}_x$ interfaces aligned with either the {110} or {211} orientations across the ensemble of simulated absorption trajectories. At each value of $c_\beta$, the $\alpha$/$\beta$ interface is computed for all trajectories. The color represents the fraction of best-fit planes whose normal vector is closer to that crystallographic orientation than to the alternative orientation considered. Black pentagram markers and their corresponding vertical lines denote the transition-state $c_\beta$ values.
• Figure 5: Free energetics and simulated hydrogenation dynamics in nanocubes. a, Helmholtz free energy as a function of the $\beta$-phase fraction ($c_\beta$) in the nanocube. Black pentagram markers denote the transition state locations for each value of the effective chemical driving, $\Delta$$\mu$. b, Average elastic energy across simulated hydrogenation trajectories, plotted as a function of $c_\beta$. The shaded area represents the standard deviation across trajectories. Black pentagram markers correspond to the same transition-state $c_\beta$ values shown in panel a for each curve. All energies are measured in units of $k_\mathrm{B}T$, where $k_\mathrm{B}$ is the Boltzmann constant and $T$ is the simulation temperature. c, Representative snapshots from absorption trajectories in nanocubes. Each row corresponds to a single trajectory at $\Delta$$\mu$ = 0.0, 0.2, and 0.5 $k_\mathrm{B}T$ (top to bottom). Snapshots are colored in terms of the density of each phase, with blue as $\beta$-$\mathrm{PdH}_x$ and red as $\alpha$-$\mathrm{PdH}_x$. Black pentagram markers additionally indicate the snapshots corresponding to the transition state. d, Fraction of $\alpha$/$\beta$-$\mathrm{PdH}_x$ interfaces aligned with either the {110} or {100} orientations across the ensemble of simulated absorption trajectories. At each value of $c_\beta$, the $\alpha$/$\beta$ interface is computed for all trajectories. The color represents the fraction of best-fit planes with a normal vector closer to that crystallographic orientation than to the alternative orientation considered. Black pentagram markers and their corresponding vertical lines denote the transition-state $c_\beta$ values.