In Situ Wide-Field Visualization of Palladium Hydrogenation.

Visualizing hydrogenation processes in palladium (Pd) in real-time is important to various hydrogen-involved applications. However, observing hydrogen diffusion of Pd was limited by its small permittivity variation, and the kinetics of lateral diffusion of hydrogen in Pd film was not reported. Here, we proposed an optical microscopy-based visualization of Pd hydrogenation from the diffusion surface to the interior by introducing a fast-response mechanical platform that transforms the hydrogen diffusion into self-organized ordered wrinkles with sharp optical contrast. This platform is a Au/Pd double layer on an elastomer, which results in directional hydrogenation from the sidewall to the interior. The kinetics of hydrogenation in the interior of the palladium along the diffusion direction was monitored in real-time. This platform will enable in situ visualization of atom/ion diffusion on metals that are crucial in energy storage and hydrogen detection.

not only help to understand the solute intercalation mechanisms but also improve the system's cyclability by avoiding catastrophic structural failure including lattice dislocations and fractures [7][8][9] . In particular, metal hydrides such as palladium (Pd) hydride are receiving increasing attention due to their fast hydrogenation kinetics at comparatively more accessible reaction conditions [10][11][12] , but this also poses a great challenge to the in-time monitoring of the transient processes.
Hydrogenation of palladium has been under intensive studies to resolve the kinetics of diffusion-induced phase transitions, which constitutes a representative class of atom and ion diffusion in solids and is closely related to the physics of lithiation of batteries 10,13 . The fast kinetics of palladium-hydrogen reaction along with accessibly environmental conditions make palladium an extraordinary choice of material for rapid absorption of a large amount of hydrogen. For example, palladium membranes received great interest with their potential to separate and purify hydrogen at high flux and exclusive selectivity. In these Pd membrane based gas separation systems, molecular hydrogen first dissociates at the palladium membrane surface followed by diffusing through the membrane and then emerges as molecular hydrogen upon rebinding of the atoms. The absorption and desorption of hydrogen in palladium is accompanied by significant volume change 14 , and monitoring strain evolution associated with the metal lattice during hydrogenation at real time could potentially provide insights into the coupling between strain-induced hydride formation and transport of hydrogen flux. Yet a direct observation of the phase transition between α-and β-phases remains a challenge, because the planar geometry of thin films often fails to translate the microscopic structural change induced by hydrogen flux permeating through the film thickness into experimentally observable quantities at a macroscopic scale.
Several visualization techniques such as the switchable mirror devices leverage on the large optical and electrical properties changes in selective metal hydrides including magnesium and rare-earth elements [15][16][17] . However, the switchable-mirror approach works on planar thin films and heavily relies on the intrinsic optical properties of mirror material to achieve large optical contrast, thus limiting its applicability. On the other hand, scanning transmission electron microscopy (STEM) 10 , electron energy loss spectroscopy (EELS) 11,18 and plasmonic nanoantenna 4 have demonstrated to be effective tools for the study of phase transformation behavior of palladium hydride on the particle level. Although they provide the capability of insights into individual nanocrystals, they inevitably require convoluted experimental setups that involve highly material-specific procedures and are not always readily accessible. A fast and effective in situ monitoring and observation of the hydrogenation process in real-time still remains highly desirable. It is now established that the mobility of hydrogen atoms in metal is many orders of magnitude larger than that of other interstitially dissolved atoms at room temperature.
Rapid transport of hydrogen into Pd leads to a considerable lattice expansion, and to accommodate the compressive stress applied by the Pd layer, the supporting PDMS substrate developed into self-organized strips and wrinkles triggered by linear and nonlinear elastic instabilities. Such diffusion-deformation process can be characterized by relevant time scales: For palladium at low concentration of hydrogen (known as α-phase), palladium atoms are arranged in face-centered cubic lattice of constant 3.891Å. With the increased supply of hydrogen gas species from the environment, the hydrogen atoms will occupy randomly at the octahedral interstices in the lattice, forming a solid mixture of PdHx.
Further increasing hydrogen concentration x > 0.60 leads to a discontinuous change to β-phase with a new lattice parameter of 4.026 Å. At thermal equilibrium, macroscopic hydrogen concentration ratios 0.03 < x < 0.60 reflect a mixture of α-and β-phases of palladium hydrides. Compressive stress is thus exerted by the Pd film to induce the formation of ripples and folds that can be monitored by a wide-field microscope under illumination. With proper selection of film thickness and stiffness of the PDMS substrate, the one-dimensional (1D) ripples act as optical gratings, whose amplitude depends on the local stress states during volume expansion of the Pd layer. A stronger amplitude of such ripple causes stronger diffraction, and the intensity of directly reflected light is reduced, as observed by intensity contrast in the image field. With this approach, we can clearly visualize the propagating front of α-and β-phases and determine their propagation speeds.
Coupled with our diffusion-deformation-diffraction framework, we are able to provide more quantitative insights into the hydrogenation kinetics and phase-dependent selfinduced stress during phase transition. To our best knowledge, it is the first time for such a pattern generation mechanism to be implemented on a hydrogenation platform to observe the diffusion and phase transition kinetics of the hydrogen in the interior of the Palladium. This approach constitutes a general framework for in situ in efficient real-time visualization of generic solutes diffusion into solids. An optical microscope was used to observe the surface deformation of a GPDP, which was placed on a gas cell (Fig. 1a). Figure 1b,c show the schematic of the surface deformation of the GPDP comprised of an Au/Pd film on a PDMS slab, which changes from a planar surface to regular wrinkles during hydrogenation. The x-axis and y-axis are defined to be parallel and perpendicular to the edge on planar directions, respectively, and the z-axis is normal to the surface (Fig. 1b). The deformation of the PDMS is assumed to be viscoelastic with Kelvin-Voigt material behavior (Fig. 1c). 1e, i). When 4% H2 with nitrogen gas (N2) was injected, uniform 1D ripples evolved from the edge of the GPDP along the direction of hydrogen diffusion (in the y-direction from the graph) and extended to the center of the film, resulting in a drastic change of reflected light intensity (Fig. 1f, j). We found that merging of the 1D ripples ( Fig. 1f), which is induced by topological defects such as elementary dislocations and disclinations 19 . Surprisingly, a sharp contrast of brightness is observed in different zones of the film (Fig. 1j), which can be attributed to the phase transition of Pd film during hydrogenation. As the hydrogen diffused from the edge to the center of the GPDP, the 1D ripple at the inner region became dark as well (Fig. 1g, k) and then transformed into two-dimensional (2D) herringbones (Fig. 1h, l). Meanwhile, the ripples are brighter than the 2D herringbones (Fig. 1h). In contrast, the surface wrinkling of a single Pd film with the same thickness on PDMS upon exposure to 4%

Fig
H2 is subject to isotropic stress which manifests aperiodic labyrinth patterns ( Supplementary Fig. 2). This indicates that the Au film capped on the top of the Pd film plays a key role on the ordered self-organization, which provides a platform to visualize the diffusion of hydrogen in Pd film.
where Ki and ti are the front mobility 22   The generation of 1D/2D patterns of the GPDP can be explained by the mechanical deformation of a thin stiff film on an elastic substrate. We first focus on the 1D ripple pattern, which is characterized by the distance between adjacent ripples defined by ripple wavelength 1 and ripple amplitude A1 (Fig. 1c). In the case of a freestanding substrate with uniform exposure, the absorption of H2 results in an isotropic volume expansion of Pd film. On the other hand, when the Au cladding forces H2 to diffuse unilaterally into the film constrained on a substrate, the diffusion-induced stress becomes anisotropic with two orthogonal components denoted as along the x-axis and along the y-axis. As the GPDP is exposed to 4% H2, with the volume inflation The ripple wavelength 1 can be estimated by minimizing the system energy, including film and bending energy of the Au/Pd film and elastic energy of the PDMS substrate, which can be expressed as 24 ： We also conduct finite element analysis using software package COMSOL to directly solve the solid mechanics equation under plane strain condition for the displacement field of a 30-nm Pd film in the form of 1D ripple, as illustrated by Supplementary Fig.   6, which is well consistent with the experiment. According to equation (4) Fig. 12a) and wrinkling amplitude Equation (5). Eventually, the information gathered from two branches led to the concentration-stress relation, which was deduced from experimental data at one particular point. However, it can be applied to any arbitrary position of the field (Fig.   3c). The fitting results suggest that H2 absorption-induced stress initially exhibits a logarithmic growth when the ratio of hydrogen atoms is low, followed by two piecewise linear increasing relations in α + β and β phases, respectively. This indicates that the palladium's uptake of hydrogen solutes may trigger a different elastic response of lattice depending on the solute concentration. After acquiring this essential relation, we once again exploited the relationship between the amplitude of the 1D ripples with various Pd thicknesses and the stress ratios 1 � (Supplementary Fig. 12b) according to equation (5). The strictly monotonic relation ensures a well-defined one-to-one mapping when the stress profile is converted to the undulation's amplitude and vice versa. The data flow was directed into the sinusoidal grating simulation to obtain light intensity change at the wavelength of 550 nm illumination on a 5-um period grating.
Again the reflected light collection was cut off at the 3rd diffraction order on account of the numerical aperture of the objective lens. Finally, we established the quantitative relation between diffusion time and reflected light intensity at any location (Fig. 3d).
The variation of simulated reflected light intensity with time shows similar trends as  . This is further validated by our modal analysis using COMSOL assuming a pre-defined 1D ripple pattern (Fig. 4c), which agrees well with the experimental result. The longwavelength 2 monotonically increases with the increasing thickness of the Pd film hPd (Fig. 4d, Supplementary Fig. 13) as that of the short wavelength 1 (Fig. 2b).
Unlike the primary buckling, the quantitative evaluation of 2 tends to be challenging without knowing the values of a priori 32 . Further insights into the 2D stress state can be gained through the measurement of the secondary wrinkling wavelength 2 .
Although our study was focused on real time visualization of hydrogenation in metal membranes using local wrinkles, our methods of retrieving stress states using wide-field optical scatterometric means in real time can be applied to a more general class of reaction-diffusion systems 34 , where the induced surface instability generates various surface patterns, as previously reported in chemical traveling waves 35 , electrodeposition 36,37 , and biological systems 38 . Because the wrinkles and folds can be easily imposed on these material systems over large areas at low cost, we expect such simple and elegant geometric effect on enhanced reflection can provide deep physical insight of monitoring strain evolution associated with the host material (such as thin solid electrolyte interphases in the lithium battery) during diffusion-reaction at real time.

Discussion
In summary, we have demonstrated that an Au/Pd double layer on a PDMS Optical measurement. The sample was placed in a gas chamber with an optically transparent window and two gas channels (Fig. 1a) at room temperature. Surface wrinkling of the GPDP during hydrogenation was observed by an optical microscope system with 10X and 50X objectives (MPLFLN10x and SLMPLN50x, Olympus, Japan), which were utilized to focus the probe light of a tungsten halogen light source on the sample and collect the backscattered light. The numerical aperture (N.A.) and work distance (W.D.) of the 50X objectives are 0.35 and 18 mm, respectively. A COMS camera (Zyla-4.2P-USB3, Andor, UK) was utilized to record the deformation process.
The concentration and flow rate of H2 are 4% and 1000 sccm, respectively.
Theoretical calculation of the 1D wavelength. Based on the minimum energy method, the wavelength of 1D deformation 1 on the system of a stiff thin film on an elastic substrate can be expressed as 39 : Where E and are the Young's modulus and Poisson's ratio, and the subscript f and s represent the thin film and substrate, respectively. For the GPDP, we assume that the Young's modulus and Poisson's ratio of the Pd film have no significant variation during hydrogenation. The stiff thin film consists of an Au and Pd film with the effective Young's modulus Eeff, defined by :