## Introduction

Metal nanoparticle-based heterogeneous catalysts play an important role in energy conversion and environmental technologies1,2. In addition to their larger surface to volume ratio, they have highly under-coordinated sites. In general, under-coordinated sites including steps and kinks can enhance the catalytic efficiency3,4,5,6 by decreasing kinetic barriers of dissociation and/or bond breaking of the reactants7. Interactions between reactants and catalysts are a key factor determining reactivity8,9 in heterogeneous catalysis. Since structure and interaction are coupled under reaction conditions, several studies reported overall shape or size changes of metal nanoparticles10,11,12,13 during catalytic processes. They observed facet rearrangement, contraction and relaxation of the bond distance, and surface morphological refacetting, and so on.

In heterogeneous catalysis, the identification of active sites14 is important in terms of understanding the catalytic mechanism and improving the efficiency of the surface catalytic reaction. Active sites have been identified as low-coordinated atoms by microscopy techniques such as scanning tunneling microscopy14 and scanning transmission electron microscopy15. Infrared spectroscopy is sensitive to interactions between catalysts and reactants in terms of chemical adsorption16 and X-ray absorption spectroscopy is useful for investigating the electronic states related to chemical bonding in the catalysts17. However, the structural changes at the active sites have not been clearly understood so far.

Bragg coherent diffraction imaging (BCDI) is sensitive to distortions of the crystal lattice, owing to the highly sensitive nature of this technique to minor modifications of the phase of a scattered wave field18,19,20. This is accomplished through careful measurements of coherent X-ray diffraction (CXD) patterns in the vicinity of Bragg peaks of the sample and computational methods21,22 to retrieve both the shape of the nanocrystals and the internal displacement from the relative phases of the interference pattern.

Here we study distortions at active sites in platinum (Pt) nanocrystals using in situ BCDI, above and below the activation temperature of catalytic methane oxidation23 as an example of catalytic process. The results show the severe crystal lattice displacement at the edges than the facets due to the adsorption of oxygen and catalytic reaction of methane. In addition, the simulations by reactive molecular dynamics (RMD) informed finite element analysis (FEA) are consistent with 3D reconstructed images from the CXD patterns.

## Results

### In situ structural evolution during the catalytic process

Pt nanocrystals were synthesized by dewetting from a thin Pt film deposited on Al2O3 substrates. (Supplementary Figure 1 shows a typical SEM image.) The study was conducted in stages, with 3D CXD measurements performed at the following steps: (1) oxygen adsorption and (2) methane oxidation. Figure 1 schematically shows the BCDI experimental setup and CXD patterns measured at the (111) Bragg peak of an individual Pt nanocrystal above the activation temperature. Here we selected the size of the Pt nanocrystals to be ~200 nm to provide a distinct deformation field distribution in a single nanocrystal within the typical spatial resolution of BCDI (~14 nm). The detailed experimental conditions regarding gas environment are described in Methods. The initial CXD pattern in H2 (Fig. 1a) showed the sixfold symmetry expected of a Pt nanocrystal with a truncated octahedral shape, with (111) and (100) facets. As the oxygen adsorption progressed (Fig. 1b, c), the center of the Bragg peak changed shape from circular to triangular, and the fringe pattern became strongly asymmetric. In particular, the first fringe showed noticeable changes, indicating that the Pt nanocrystal deformed almost through the entirety of its volume24. The maximum distortion was observed in Fig. 1d when CH4 was introduced. The distortion continued in Fig. 1e throughout the chemical reaction until the catalytic process completed. Strain release was evident in the CXD pattern in Fig. 1f. For comparison, the patterns recorded below the activation temperature did not show any notable changes (Supplementary Fig. 2).

To understand how distortion evolved during the catalytic process, the Pearson correlation function25 was applied to the total three-dimensional (3D) CXD patterns. The Pearson correlation coefficient for CXD patterns is

$$\rho \left( {A,B} \right) = \frac{1}{{N - 1}}\mathop {\sum }\limits_{i = 1}^N \left( {\frac{{A_i - \bar A}}{{\sigma _A}}} \right)\left( {\frac{{B_i - \bar B}}{{\sigma _B}}} \right),$$
(1)

where Ai and Bi are the scattering intensity values for a particular pixel in the pattern, $$\bar A$$ and $$\bar B$$ the mean values of the scattering intensities, and σA and σB the standard deviations, for the two CXD patterns, A and B. The sum is evaluated over 3D CXD patterns and ρ(A,B) is computed for the selected area around the first fringe where shows maximum distortion. (See Supplementary Fig. 3.) Fig. 2a, b show contour slices through the CXD patterns (Fig. 1a, b, respectively) with the red contour identifying the first fringes. The cross-correlation map in Fig. 2c was computed for the CXD patterns measured in various gas environments by using Eq. 1, and detailed procedure is described in Methods. Gas environments together with the exposure times are indicated on the x and y axis, and the experimental conditions for Fig. 1a–f are also indicated on the map with black arrows. Time 0 indicates the start of each gas flow. The correlation coefficient, 1 means total positive linear correlation, 0 means no linear correlation, and −1 means total negative linear correlation. Immediate distortion appeared after oxygen gas was introduced. The original diffraction pattern was recovered after ~22 min in CH4. This reversion can be attributed to the available oxygen being consumed by catalytic oxidation. Gas analyses were carried out to check the catalytic reaction and resultant products (CO2 and H2O).

### Reactive molecular dynamics simulation

To elucidate the reaction mechanism of methane oxidation on Pt, large-scale RMD simulations26,27 were performed. Snapshots of the atomic displacements of Pt nanocrystals in H2, in O2, and in CH4 after oxidation, are shown in Fig. 3a–c, respectively. In Fig. 3a, we observed limited interactions between Pt and H, consistent with the experimental observations. Figure 3b shows the effects of oxidation of the nanocrystal at edge and corner sites, where Pt atoms are under-coordinated, after exposure to O2 for 100 ps. Molecular oxygen also physisorbed on the surfaces of the Pt nanocrystal. To simulate methane oxidation in limited adsorbed oxygen environment, we removed un-adsorbed O2 molecules, while adsorbed O2 molecules and bonded O atoms were retained. We then introduced CH4 molecules and ran additional isothermal-isobaric dynamics for 45 ps. Figure 3c shows the structure of the particle after 44 ps. We observed the bonding of CH4 molecules to dissociated O atoms at edge and corner sites (shown in Supplementary Fig. 4). However, we did not observe the final products escaping the surface of the nanocrystal within the short timescales of our RMD simulations28. Notably, only a fraction of adsorbed oxygen atoms was an active site for methane oxidation owing to steric hindrance. Thus, we calculated the ratio of adsorbed methane to oxygen atoms (CH4/O) on the Pt nanocrystal in the RMD simulation in Fig. 3d. The CH4/O adsorption ratio was fitted to an inverse exponential, which was extrapolated to infinite time to yield an adsorption ratio of 0.398 ± 0.003. Although the kinetics at picosecond timescales of atomic level processes are difficult to translate into experimental particle sizes, the resultant values of local atomic displacements are expected to be similar for larger Pt nanocrystals.

### 3D imaging and RMD-informed finite element analysis

The atomic displacements obtained from the measured CXD patterns by phase retrieval process are compared with the calculated results in Fig. 4. Figure 4a–d show 3D images and cross-sectional images from the CXD patterns shown in Fig. 1a, b, d, f, respectively. 3D images are colored by the local displacement field at the surface and at vertical cross-sections with reference to a perfect Pt lattice. Red (positive sign) indicates the projected displacements along the [111] direction, u111, and blue (negative sign) implies the opposite direction. Note all the displacements shown here are after the refractive index correction29. (See Supplementary Fig. 5.) The residual distortion in the as-synthesized crystal in Fig. 4a is a maximum value of u111 as 7% of lattice constant of Pt111. Figure 4b shows strong contraction at the edge due to chemisorbed O atoms from dissociation of O2 molecules with maximum u111 as 20% of the lattice constant. Because the direction of the projected displacements starting at the edge faces toward the interior of the Pt nanocrystal, this indicates contraction. (Detailed interpretation can be found in Supplementary Fig. 6.) Different projections of the displacement field arisen from the edges can be measured at other Bragg peaks30. In Fig. 4c, the greatest distortion is detected because of the bonding of CH4 molecules to dissociated O atoms. The maximum u111 value is ~30% of the lattice constant. The cross-sectional images in Fig. 4b, c clearly demonstrate that contraction originated at the edges is propagated to the interior of the crystal. As shown in Fig. 4d, after methane oxidation ended, the contracted lattice was released. (See Supplementary Fig. 7 for expanded time range.)

The CXD image of the nanocrystal was imported into an RMD-informed finite element model, and suitably meshed. We emphasize that FEA was performed on the density of the CXD image with suitable substrate constraints and input forces estimated from the RMD simulation, as shown in Fig. 4e. The force exerted by an adsorbed O atom on a Pt atom was determined from the RMD simulation to be 1.17 × 10−10 N. Assuming 14.8% coverage of oxygen (see Methods) on the edge sites at the top of the nanocrystal (having 14.99 Pt atoms per nm2), the total compressive stress PMD was determined to be 259.74 MPa. The steady-state FEA solution for this system revealed a maximum u111 of 0.04 nm (Fig. 4g). Further adsorption of methane at active oxygen sites resulted in an additional compressive force on a Pt atom of 1.12 × 10−10 N. With an adsorption ratio of 0.398 and methyl coverage of 5.88%, an additional compressive stress of 98.79 MPa is applied at the edge sites on the top of the nanocrystal. Figure 4h shows steady-state FEA solutions resulted in a maximum u111 of 0.07 nm (consistent with the experimental observations in Fig. 4c). In addition, the steady-state displacement field extended ~50 nm into the particle interior. The similarity of the FEA to the BCDI results confirmed the RMD simulations and indicated that the under-coordinated corners and edges of the Pt nanocrystal acted as preferential adsorption sites for oxygen.

## Discussion

We note that there were not enough final product formation events on the short RMD timescale to achieve a statistically reliable estimate of the direction of the force (compression vs. tension) owing to methane adsorption. The BCDI experimental reconstructions clearly indicated that addition of methane induced compression of Pt. Hence, we assumed a compressive force in the FEA simulation. The obtained match in displacement magnitudes and distributions within the crystal between RMD-informed FEA and BCDI is a remarkable result. This finding, (1) validates the hypothesis that adsorption events on Pt edge sites cause the observed displacement field. (2) Furthermore, it is likely that the top edge sites of the Pt crystal are most active. (3) The simulation spanned several length scales and remained consistent with the experimental observations, emphasizing the strength of this integrated approach to investigating nanocatalysis behavior.

In addition, to estimate exact strain field distribution inside the crystal, the strain (∂u111/∂x111)25 was calculated for 3D images in Fig. 4. Supplementary Figure 8a–d show the 3D images in Fig. 4a–d with front view of (100) facet (on the left) and vertical slices (on the right). The highly strained area (u111/∂x111 > 2 × 10−3) in O2 locates at the corner of (100) facet with tensile strain (in red, positive values) on the left and compressive strain (in blue, negative values) on the right, and the area enlarges with introduction of CH4. This anisotropic strain might be clue for shape changes observed during general oxidation processes10,11,12,13.

In conclusion, using in situ BCDI, we observed deformation of a single Pt nanocrystal with a considerable compressive strain starting at the edge indicating localization of active sites during catalytic methane oxidation. Contraction at the edges arises due to dissociated O atoms and the deformation becomes stronger when CH4 molecules bond to the dissociated O atoms during the chemical reaction with CH4. The deformation field distribution arising from the interaction forces between the reactants and the Pt catalyst was confirmed by RMD-informed FEA. Our work identified the active sites underlying atomic-scale catalytic activity, where it can induce structural changes of nanocrystals during the catalysis.

## Methods

### Sample preparation

Pt nanocrystals were prepared by dewetting from Pt films for 14 h at 1700 ℃ under argon flow in a tube furnace (GSL-1750X, MTI Corporation). Pt films were deposited on sapphire (0001) substrate with an electron beam evaporator. A typical scanning electron microscope (SEM) image of a sample is shown in Supplementary Fig. 1. SEM measurements were performed with a scanning electron microscope SNE-4500M (SEC).

### Bragg coherent X-ray diffraction imaging experiments

Focused coherent X-rays with a wavelength of 0.1377 nm from a Kirkpatrick–Baez mirror at the 34-ID-C beamline in Advanced Photon Source, USA, illuminated isolated samples mounted in a sample chamber under gas flows of 1% H2, 20% O2, and 1% CH4 with a N2 base gas flow of 50 mL per min over various temperatures. Before and after the catalytic processes, the CXD patterns were recorded in a flow of 1% H2 in N2 for ~30 min to clean the Pt surface. The samples were exposed to a flow of 20% O2 in either He or N2 for oxygen adsorption and to a flow of 1% CH4 in either He or N2 for methane oxidation. Before introducing CH4 into the sample chamber, the remaining O2 gas was completely removed by evacuation. The CXD patterns were measured with a Timepix detector (Amsterdam Scientific Instruments) with 55 × 55 μm2 pixel size located ~0.65 m away from the sample. Three-dimensional diffraction data were collected as rocking curves of the sample tilt angle in steps of 0.01° with a total of 61 frames.

At the P10 beamline in PETRA III, Germany, coherent X-rays with a wavelength of 0.1486 nm were focused by compound refractive lenses to illuminate the Pt nanocrystal samples. The samples were mounted in a sample chamber under a gas flow of 1% H2, 20% O2, and 1% CH4 in a He base gas flow at 100 mL per min with varying temperature. The gas exchange process was same as above. CXD patterns were measured with a Lambda detector (X-Spectrum) with 55 × 55 μm2 pixel size located ~1.83 m away from the sample. Three-dimensional diffraction data were collected as rocking curves of the sample tilt angle in steps of 0.01° with a total of 61 frames.

### Phase retrieval algorithm

We used a phase retrieval package that has been used extensively31. After loading CXD patterns from BCDI measurements with a random phase, 620 iterations with constraints consisting of error reduction and difference map (hybrid input-output) combinations were progressed with guided analysis (GA). The GA method helps to select the best reconstruction from the lowest sharpness metric, which is the summation of the absolute value raised to the fourth power for the reconstruction result. This process was performed for five independent reconstructions with three generations, where the previously used reconstruction was set as the seed for the next one.

### Mass spectroscopy measurements

The gas analysis was carried out with a mass spectroscope (Prisma Plus™ QMG220) and mass flow controllers (MFCs). To measure the final products with enough S/N, the Pt powder (200 nm) in capillary was used. Below and above the activation temperature, 20% O2 gas in a N2 base gas was flowed at 50 mL per min with a MFC for 40 min, and then flushed out. After flushing, the sample was exposed to a 1% CH4 gas flow in a N2 base gas flowed at 50 mL per min with a MFC for 40 min. CD4 gas was also used for identifying the final products.

### Cross-correlation analysis

Cross-correlation analysis was applied for observing changes in the CXD patterns in various gas environments with time. The cross-correlation map was obtained by the Pearson correlation function, which calculates the covariance of two variables divided by the product of their standard deviations. We focused on the first fringe region of the CXD pattern in Fig. 2a and Fig. 2b (selected areas marked as dashed boxes in the Supplementary Fig. 3a, b) because the region showed maximized distortion generated by strain throughout nearly the whole volume of the Pt nanocrystal25. Note that the selected regions were not limited to the two-dimensional areas but to the 3D volume in the integrated 3D CXD patterns. The cross-correlation maps for the four selected regions , , , and are displayed in the Supplementary Fig. 3c–f, respectively. The correlation coefficient implies the average of the normalized intensity correlation at each pixel position in the selected region.

### Reactive molecular dynamics simulation

Reactive molecular dynamics simulations were performed with the use of the idealized Pt nanocrystals (~10 nm diameter, 250,000 atoms) created in the shape of a truncated octahedron. All simulations were performed within the reactive force field framework with the potentials published by Singh et al.27 The Pt nanocrystal was equilibrated at 0 K through an energy minimization before being heated up to 300 K in 30 ps. The particle was subsequently heated to 600 K in the presence of H2 in 30 ps and then held at that temperature for 100 ps. The same procedure was used for the particles in an oxygen environment. The oxidized Pt structure was then placed in a CH4 environment at 600 K and dynamics were run for 45 ps. All simulations were performed under isothermal-isobaric conditions using the Nose–Hoover thermostat and barostat as implemented in the LAMMPS package28. Equations of motion were integrated over a timestep of 0.1 fs by the verlet integrator. Atomic structures were rendered by the Ovito package32.