Single alloy nanoparticle x-ray imaging during a catalytic reaction

We have imaged a single alloy catalyst nanoparticle at work, resolving its facet surface composition.

PtRh alloy particle was in addition determined from the d-spacing at 700 K using Bragg's law and Vegard's law. The  , λ being the wavelength of the x-ray beam and the position of the (111)-Bragg peak determined from the experiment. Following Maisel et al. and assuming that the binary PtRh alloy does not exhibit a miscibility gap (21), the PtRh composition can be estimated from Vegard's law, Here, is the concentration of platinum in the alloy particle. The lattice constants at 700 K are = 3.9387 Å and ℎ = 3.8177 Å for Pt (46) and Rh (47), respectively. In the experiment, the Bragg peak position was determined to be = 17.873° with an x-ray wavelength of λ = 1.378 Å, yielding a mean alloy composition of Pt58.4Rh41.6, close to the nominal composition and the results from the EDX analysis discussed below.
To ensure the re-localization of nanoparticles pre-selected in the SEM (35), reference markers were deposited in close vicinity by electron-and ion-beam-induced deposition (EBID/IBID) of a Pt precursor gas. In a three-level hierarchical way, additional guiding markers with increasing size and thickness were applied towards the edges of the STO single crystal substrate, e.g., see, a zeroorder marker in Fig. S2, facilitating a simplified guided search across the PtRh nanoparticle landscape. Python and Matlab scripts were employed to translate the stage positions of the markers and nanoparticles in the SEM to the stage positions at the ID01 x-ray beamline and in the AFM.
The Python script permits a direct import and export of the coordinate positions from the stage and the sample to the beamline operation system. PtRh nanoparticles were selected based on their size, shape and isolation to avoid parasitic scattering from adjacent particulates. Second order markers were placed within a distance of 50 µm from the selected PtRh nanoparticles to lie within the scanning range of the piezo stage at the x-ray beamline. The distortion of the x-ray scanning image in Fig. S2d as compared to the SEM image in Fig. S2c is due to the sample tilt to fulfill the Bragg condition. This implies that in specular geometry the piezo move parallel to the x-ray beam is accompanied by a change in sample height translating into an additional move along the x-ray beam, resulting in the apparent stretch of the x-ray scanning image. Further details on the marking, strategy of marker arrangement and a re-localization protocol can be found in a previous work (16).
All SEM images were obtained at an acceleration voltage of 5 kV. The lower resolution SEM images of the hierarchical guiding markers (Fig. S2) were taken with an Everhart-Thornley secondary electron (SE) detector. The higher magnification images of the nanoparticle in Fig. 1 were obtained with the through-lense detector (TLD) in the SE mode. Ex situ AFM topographic images were obtained in tapping mode in air using an oxide-sharpened silicon cantilever (35). The total size of the overview image in Fig. 1

Bragg CDI data analysis
The 3D reciprocal space intensity distribution was obtained by linear interpolation of diffraction patterns on a Cartesian reciprocal space Qx, Qy, Qz grid. Before interpolation the average background on the level of three photons was subtracted (from the Be dome, the surrounding gas or the substrate) and less than 0 counts were set to zero. Slices of the intensity distribution reported in Fig. S5 show clear interference fringes arising from the coherent diffraction of a faceted single particle. Small changes in the reciprocal space intensity distribution are noticeable, and are related to shape and strain field modification in the catalytic nanoparticle under different gas atmosphere conditions.
In practice, since the phase φ(r) is reconstructed with an unknown offset, it was set to zero at the center of mass of the support obtained using a cutoff of 55%. Next, the phase was unwrapped and the displacement field uz(r) was calculated (see Fig. S6 and Fig. S8). To determine the strain, the derivative of the displacement field was taken as it is shown in Fig. S8 and Fig. S9.
The real space resolution was determined by two different methods. The first one was the Phase Retrieval Transfer Function (PRTF) (48), with resolution values determined at a threshold 1/e. The second approach was based on the procedure proposed in (49). In this method, the resolution is defined as the FWHM of the point spread function (PSF) that was obtained, in our case, by the blind deconvolution algorithm (50,51) which was implemented in MATLAB software.
Importantly, the number of iterations was small and was determined as a first minimum of the amplitude mean-square error function. That gave us from 10 to 15 iterations in each gas conditions case. This deconvolution process was applied to the amplitude function (threshold 0.55). The PSF from the amplitude of the object represents the degree of blurring for the particle along each direction. To determine the FWHM of the PSF in different directions they were fitted by Gaussian functions (see Fig. S12 and Table S3).

Determination of facet dependent strain
The outer layer of each facet of the reconstructed nanocrystal was isolated in order to extract facetresolved strain histograms and compare them for different gas environments (Fig. S11). The data segmentation follows the workflow described in (52) with adaptations to the particular problem of performing statistics on the surface strain. It takes as input the reconstructed modulus and strain obtained by phase retrieval, as well as the isosurface value defining the surface voxel layer of the nanocrystal. The analysis can be divided into two parts: first, finding the number of independent facets, labelling them and getting a first estimate of the equations of planes parallel to them. The second step consists in refining the plane parameters by matching it with the reconstructed nanocrystals surface and isolating the voxels belonging to each facet.
In order to identify and label facets, the modulus is first meshed using Lewiner marching cubes (53), and then smoothed using Taubin's smoothing (54). Each triangle of the mesh is described by its vertices and normal. The normals are weighted by the surface of their respective triangle. Then, a density map of the same size as the array of normals can be created by summing for each normal the neighboring normals weighted by their distance, if they are closer than a certain radius. The next step is to project this 4D data (three positions and the density) using a stereographic projection (55), which provides two 2D plots corresponding to the projections from the South Pole and North Pole, respectively. Densities are then inverted, and new maps corresponding to the distance of the data to the background are calculated. From these distance maps, the local minima are identified, and labels are assigned to them. Then, watershed segmentation is applied in order to assign a label to each point of the projections (label 0 being the background). The duplicity of labels (two labels for a single facet) is checked using the position of the corresponding points on the stereographic projection. Now that the facets have been identified uniquely and labelled on the stereographic projections, one can go back to the corresponding normals, mesh vertices and finally voxels using array indices which are preserved during all calculations. Note that these voxels may not anymore exactly correspond to the original object due to smoothing. They are used as an initial population of voxels belonging to a particular facet (label) in order to estimate the equation of a parallel plane.
The first estimate of the plane equation is determined by minimizing the distance of the label's voxels to it. Then, the plane is translated along its normal in order to match it with the surface voxel layer of the nanocrystal, as defined by the isosurface value. The list of surface voxels belonging to the facet is updated using their distance to the plane, and the plane equation further refined. Finally, the crystal edges are isolated using a threshold on their coordination number, and the corresponding voxels are excluded from the list of voxels belonging to the facets (labels). The analysis script for the determination of the facet dependent strain is available on public repositories (56). A similar procedure to determine facet orientation dependent strain was also used in (57).

Structural models
The bulk structures of PtRh alloys have already been studied in the literature and it has been found that -at T = 0 K -the most stable structure for a 50:50 PtRh alloy is the so-called "40" structure.
However, it has also been found that these ordered bulk alloy structures already become unstable at temperatures below 300 K, with random alloys becoming more stable in free energy (21).
Our computational study does therefore not aim at determining the energetically most stable bulk composition for certain experimental conditions and compositions. Instead, we start with a fixed bulk composition and investigate the possible surface segregation in the 1 st and 2 nd surface layer as a function of external conditions. As the bulk structure, we focus on L10 Pt0.5Rh0.5, because it is similar to the experimental composition (Pt60Rh40) and because it is a simple structure that allows the construction of surface and interface models with relatively small unit cells. The surfaces fcc(100) and fcc(111) were constructed using the optimized bulk alloy to the lattice constant of 3.85 Å as slab models, which were separated by at least 15.5 Å of vacuum.

Calculations of the stability
The energetic stability of surface models, expressed by Gform, the Gibbs free energy of formation, is always computed with respect to a stoichiometrically terminated slab with bulk composition (typically Pt50Rh50): Here, is the total energy of the slab under consideration, , ℎ is the total energy of the stoichiometric reference slab. is the number of oxygen atoms, 2 is the energy of the oxygen molecule and ∆ 2 is the chemical potential of the oxygen molecule at 700 K and 2 mbar reference pressure relative to the value at 0 K, which is ∆ 2 = -0.92 eV. Δ is the number of Rh atoms that are exchanged by Pt with respective to the reference structure (Δ can also be negative) and  Tables S4-S7. A second layer composition of 100% Rh (75%) for the (100) ((111)) surface is in many cases energetically degenerate to the stoichiometric case, but the calculated average strain disagrees with the experimental values, ruling out this configuration (see Tables S4 and S5).
Effect of the slab thickness in relative stabilities and strain The relative stability of PtRh alloys was calculated using equation S1, where 100-or 111-clean surfaces with a Pt/Rh ratio of 1:1 were used as references. Table S6 shows the mean strain averaged over 2 nm thickness and relative stabilities of PtRh alloys with different number of layers. While relative stabilities appear to be unaffected by the number of layers used (up to a difference of 0.02 eV/surface atom), the mean strain is more sensitive. 9-layer slabs deviate up to 0.07% when compared to 18-layer slabs, while 11-layer slabs appear to be closer to convergence without a significant impact in computational performance, deviating only up to 0.04%. For this reason, strain and relative stabilities were computed using 11-layer slabs for (√2 × √2)R45° and (2×2) unit cells.
For structures in which a RhO2 overlayer was also included (Tables S8 and S9) For instance, the adsorption of three oxygen atoms along with Rh segregation has a deviation of around 0.12 eV/surface atom between PBE-D3 and BEEF-vdW. However, predictions made regarding the most stable structure and changes in computed mean strain are largely similar. This corroborates the use of PBE-D3 and indicates that the result regarding mean strain and stability do not depend strongly on the functional, at least for the functionals studied herein.
While the calculated average strain values of different slabs depend on the exchange and correlation functional used for the structure relaxation, deviations appear to be systematic.
According to Table S7, the mean strain of structures relaxed with the PBE-D3 functional are 0.05-0.12% higher than those relaxed with the BEEF-vdW functional, however the mean strain referenced to a clean slab with a layer composition of 50% Pt and 50% Rh does not exceed a difference of 0.02% between different functionals. This means that changes in the mean strain due to segregation or molecular adsorption are predicted more similarly with different functionals.
RhO2-thin oxide films on the 100-and 111-alloy surfaces Models of 100 and 111 PtRh surfaces with an RhO2 overlayer are shown in Figs. S14 and S15 and were constructed as in previous work on RhO2 overlayers on Rh and RhPt alloys (31,58).
Specifically, for 111, we use a 7 × 7/8 × 8 supercell. For 100, we use a √2 × 7/2 × 8 supercell (57). The energy difference between different terminations in the first metallic layer below the RhO2 layer is much lower than energy difference for clean surfaces (Tables S8 and S9). This can be explained by the fact that the less stable alloy terminations are usually more reactive towards the RhO2 overlayer, which partially compensates the different stabilities of clean surfaces.
Consequently, no clear conclusion is reached, based on calculations alone, regarding the composition of the interface.
When the RhO2-overlayer is included in the calculation of the mean strain, high values of >3% are obtained. This is because the distance of the Rh-atoms in the RhO2-layer with respect to the metal atoms in the next metal layer is on the order of 3 Å, which is an increase of around 50% with respect to the metallic bulk spacing that is around 1.9 Å for 100 and 2.2 Å for 111.
When the RhO2-overlayer is not included in the calculation of the mean strain, mean strain values are obtained, which are on the same order as those of clean surfaces. The dependence of the strain on the composition, however, is similar to clean or oxygen surfaces, e.g. a higher Rh content leads to lower strain and higher Pt content to higher strain. The adsorption free energy for a given surface was thus obtained from the adsorption energy ∆ computed for that surface, by adding the correction for adsorption energy derived from experiments plus the correction from thermal motion of the nuclei: The results are compiled in Table S10 and S11 and the most stable structures for the 111-surfaces are additionally shown in Fig. S16. Figure S17 shows the atomic structure of the most stable computed 111 surface with a quarter monolayer of CO. We find that, at the experimental conditions, surfaces are predicted to be clean, Pt-terminated surfaces. The most stable structure containing adsorbed CO in a 111-surface, is only 0.04 eV less stable. In this structure, a single Rh atom per 2×2 cell is in the first layer and one CO molecule is adsorbed in the on-top position on this Rh atom.
PtRh Nanoparticle/STO interface energetics The computational model (shown in Fig. S18) is constructed using the Ti-terminated STO(100).
The supercell is 2×7√2 -Pt(111) on √2×6√2-STO(100). According to Table S12, the mean strain values are similar to those obtained for clean PtRh slabs without the STO support (Table S5). We also observed that relative stabilities per surface atom of 50% Pt / 50% Rh, pure Pt or pure Rh at the interface are very similar, so that there is no clearly preferred termination. The orientation of the metal-support interface is illustrated in Fig. S18.

Surface Energy calculations
Surface energies were determined from a series of slab calculations with increasing thickness (58) to obtain the bulk limit by extrapolation. For Pt-terminated 111 and 100 surfaces, we obtain 145.6 and 170.1 meV/Å 2 , respectively. These values differ by only 1 meV/Å 2 from those of Pt and the unit cell of the alloy, which means that the difference to clean Pt surfaces is only due to the lattice constant of the alloy. The ratio of the surface energies 111/100 is 0.86. Adhesion energies were computed for the interfaces described above. If these adhesion energies are referenced to the most stable clean metallic surfaces (Pt-terminated) then we obtained -105.6 meV/Å 2 for the Ptterminated interface and -108.1 meV/Å 2 for the stoichiometrically terminated interface.

Fig. S1
The geometrical directions are defined as indicated in the figure, z corresponds to the 111 direction.
Inside the Be dome, Ar, CO, and O2 atmospheres are established by a computer-controlled gas mixing cabinet with mass flow controllers.

Fig. S5
Reciprocal space cuts through the 3D intensity distribution from the PtRh nanoparticle in three different directions shown in the inset.   Cross sections through the reconstructed PtRh nanoparticle for different gas conditions as defined in the top inset. Each column displays the reconstructed amplitude, displacement, and strain for a particular gas environment.

Fig. S9
Amplitude distribution in the reconstructed PtRh nanoparticle as a function of the gas environment shown for slices at different height levels as defined in the left inset. For the top slice of +20 nm we show the contour plot that is drawn around the initial case of the particle at Ar (I) conditions.
The same contour plot is drawn for other gas conditions. The rounding of the top part of the particle is well seen in the case of Ar+CO (IV) gas conditions.

Fig. S10
Strain distribution in the reconstructed PtRh nanoparticle as a function of the gas environment shown for slices at different height levels as defined in the left inset.        Tables S1-S12

Table S1
Gas environment before, during and after the operando CXDI experiment.

Table S3
Spatial resolution calculated using the PRTF and the PSF for the reconstructed PtRh nanoparticle, Figure S12.

Table S10
Overview of the theoretical PtRh alloy average strain values on a 100 facet in a (√2 × √2)R45° unit cell. 11-layer slabs were used as models. Reference structures are marked in bold. CO adsorption is evaluated at 700 K and 4 mbar.