Imaging the facet surface strain state of supported multi-faceted Pt nanoparticles during reaction

Nanostructures with specific crystallographic planes display distinctive physico-chemical properties because of their unique atomic arrangements, resulting in widespread applications in catalysis, energy conversion or sensing. Understanding strain dynamics and their relationship with crystallographic facets have been largely unexplored. Here, we reveal in situ, in three-dimensions and at the nanoscale, the volume, surface and interface strain evolution of single supported platinum nanocrystals during reaction using coherent x-ray diffractive imaging. Interestingly, identical {hkl} facets show equivalent catalytic response during non-stoichiometric cycles. Periodic strain variations are rationalised in terms of O2 adsorption or desorption during O2 exposure or CO oxidation under reducing conditions, respectively. During stoichiometric CO oxidation, the strain evolution is, however, no longer facet dependent. Large strain variations are observed in localised areas, in particular in the vicinity of the substrate/particle interface, suggesting a significant influence of the substrate on the reactivity. These findings will improve the understanding of dynamic properties in catalysis and related fields.

The BCDI scans shown in this work were collected during two CO oxidation cycles in reducing conditions (RC2 and RC3) and one cycle in stoichiometric conditions (SC4) for NP300; one in reducing conditions (RC1) and one in stoichiometric conditions (SC6) for NP650. Since all the particles were measured on the same substrate, NP650 also experienced 3 stoichiometric CO oxidation (SC1, SC2 and SC3-SC3', χ = 2) cycles before the first Ar measurement and one oxidizing cycle (OC1, χ = 1), while NP300 underwent 3 stoichiometric CO oxidation (SC1, SC2 and SC3-SC3'), 1 oxidizing (OC1) and 1 reducing (RC1) CO cycle before being measured (χ = 10). The first measurement in Ar was preceded by a 37 minutes reduction of the catalyst at 450 • C in 4% CO for NP650 (see S702 → S710 in Table  S1), and a CO oxidation in CO excess for NP300 (see RC1 in Table S1), implying that the surface of the NPs was most likely free of O 2 adsorbates in the initial state for both NPs. Finally, 19 hours separate the two cycles shown for NP650. During this time interval, all the measurements were carried out on NP300: 2 reducing (RC2 and RC3) and 2 stoichiometric cycles (SC4 and SC5).     Table S3 show the strain evolution in 2% O 2 and Ar atmosphere for a third NP, NPD1, which was measured before NP300 and NP650. Note that the corresponding BCDI scans (S278 for Ar and S339 for Ar + 2% O 2 ) were collected at the beginning of the first stoichiometric cycle and correspond to the first exposure of the sample to a gas mixture containing oxygen (see Table S1). Unlike NP300 and NP650, this NP is defective and contains a mixed-type dislocation (Fig. S2c). Despite the presence of this defect and the initial "pristine state" of the NP, the strain evolution during O 2 exposure is relatively consistent with the trends observed in the defect free NPs. In particular, the {1 0 0} and {11 1} and to some extent the {113} facets experience a significant relaxation. In addition, the initial surface strain is also quite similar to the one observed in NP650 and NP300. The differences in the initial strain distribution can be attributed to the different shape of the NP (large truncated (0 01) facet for instance) and to the presence of a mixed dislocation.   S3 gives an overview of the scans measured during the heating ramp carried out in Ar atmosphere. The heating ramp was set to 25 • C/min, several data points were measured during the heating of the sample. Therefore, it took approximately 415 minutes to reach the reaction temperature of 450 • C. In situ coherent x-ray diffraction measurements. 111 Pt Bragg peak of a 300-nm diameter Pt particle at 450 • C (NP300), as a function of the in-plane coordinates of the scattering vector q (qx and qy, qx being along the x-ray beam) and for different gas flows: a Ar, b 2.5% O2 and Ar, c CO oxidation: 12.5% O2, 25% CO and Ar and d 12.5% O2 and Ar. Figure S4 displays coherent x-ray diffraction measurements as a function of the in-plane coordinates of the scattering vector q (q x and q y ; q x ,q y and q z being along the incident x-ray beam (downstream), outboard and vertically upward, respectively) for different gas compositions for NP300: a) Ar, b) 2.5% O 2 and Ar, c) 12.5% O 2 , 25% CO and Ar and d) 12.5% O 2 and Ar. The third gas flow corresponds to CO oxidation in stoichiometric conditions (CO + 1 2 O 2 → CO 2 ). All the diffraction patterns display well defined streaks indicating the faceted nature of the NP surface. The diffraction patterns are all asymmetric along the q x direction, reflecting the asymmetry of the local strain distribution inside the investigated particle. Interestingly, large changes are observed in the vicinity of the 111 Bragg peak during CO oxidation (see the first fringes in Fig. S4c). These changes arise from local structural variations and suggest that the structure of the Pt particle strongly evolves during CO oxidation. Several methods can be used to estimate the spatial resolution. The resolution of the reconstruction was first estimated using the Phase-Retrieval Transfer Function (PRTF) [1,2]. PRTF in Bragg coherent x-ray imaging is defined as:

Figures S2 and
where q is the scattering vector magnitude and corresponds to the radial distance from the center of the diffraction pattern. The summations are over all q voxels that are contained in the shell q i .Õ(q) is the inverse Fourier Transform of the reconstructed object and I(q) is the measured intensity. PRTF reveals the similarity between the amplitude of the retrieved pattern and the measured pattern with respect to q. This leads to a spatial resolution of 10.5 nm.   Figure S6 for the choice of this value for the isosurface) of the maximum Bragg electron density of a 650-nm diameter Pt nanoparticle (NP650) at 450 • C and for different gas mixtures: a Ar, b Ar + 2% O2, c Ar + 2.5% O2, d Ar, 2.5% O2 + 25% CO, e Ar, f Ar + 12.5% O2, g Ar, 12.5% O2 + 25% CO and h Ar + 25% CO. The left (right) panel corresponds to the first (last) measurement of the corresponding gas mixture. During condition a and e only a single measurement was taken and is thus displayed. The direction of the scattering vector q111 from several fields of view is indicated for some images of the top row (condition a).

S12. SENSITIVITY OF BCDI TO LATTICE DISPLACEMENT AND STRAIN
BCDI allows to reconstruct a 3D complex image of isolated objects such as NPs. Its amplitude corresponds to the electron density of the object, while its phase corresponds to a projection of the 3D displacement field u(r) onto the scattering vector (111, in the present work). In the kinematic approximation of scattering, which is fully justified here because we study small crystals (<1µm), the scattered intensity is the square modulus of the Fourier transform of the atomic scattering factor: where the integration is performed over the illuminated volume, f(r), q and r being the atomic scattering factor, the scattering vector and the positions of the atoms, respectively. The Bragg geometry probes the crystalline order and coherent X-rays can be used in Bragg geometry to investigate the deviation of the sample from a perfect crystal order.
For an imperfect crystal, one can define r 0 the positions of a perfect lattice that approximates the crystal and u(r) the displacement of the atoms from the perfect lattice such that r = r 0 + u(r) (see Fig. S10). Now let's consider a Bragg reflection with a reciprocal space vector g (defined on the perfect lattice that approximates the crystal). We focus on a region of the reciprocal space (RS) in the vicinity of g: the phase factor defined in the exponential of Eq.2 can be decomposed as follows: The third term in Eq. 3 can be neglected if (q -g).u(r) << 1 (Takagi's approximation), which is equivalent to assuming small distortions of the lattice and a restricted extent of the RS, two perfectly reasonable assumptions in the present work. This gives: Here, we consider only non-resonant scattering, such that the atomic scattering factor f(r) is essentially the electron density of the sample ρ(r), while the modified scattering factorf (r) is referred as the complex electron densityρ(r): its modulus is the physical electron density while its phase encodes the projection of the displacement field onto the diffraction vector g.
This displacement field u(r) contained in the phase term: φ = g.u(r) can be understood by considering a block of material which is displaced from the rest of the lattice by a vector u(r) as illustrated in Fig. S10. The phase of the x-ray wave scattered by this block of atoms is shifted relative to the rest of the reference crystal by an amount φ = g.u(r) provided that a complex image of the sample is obtained, the phase shift appears in the reconstructed image as a region of complex density with the same amplitude but a different phase: The strain is then simply a derivative of the reconstructed displacement. For more information, please refer to Refs. [4,5]. Note that the strain field energy (see Supplementary Fig. S11(c)) is higher for NP650 compared to NP300. This is maybe due to the larger size of the particle.   FIG. S12: Comparison between experiment and simulation for NP300. a, c 200 nm simulated nanoparticle with the same faceting as NP300 and relaxed by energy minimization seen from two different field of views. b, d Experimental 111 strain field measured in Ar atmosphere for NP300 and seen from the same field of views.

S16. DISPLACEMENT
FIG. S13: Slice of the displacement field. Slice through the center of NP300 showing the evolution of the displacement field u111 for the first and last measurements of several gas conditions: a 2.5% O2, b 12.5% O2, c 2.5% O2 + 25% CO and d 12.5% O2 + 25% CO.
FIG. S14: Slice of the strain field. Slice through the center of NP300 showing the evolution of the strain field 111 for the first and last measurements of several gas conditions: a 2.5% O2, b 12.5% O2, c 2.5% O2 + 25% CO and d 12.5% O2 + 25% CO. S17. AVERAGE SURFACE DISPLACEMENT AND STRAIN COMPUTED USING THE FACET ANALYSER PLUGIN.    Figures S16 and S17 and Tables S6 and S7 further highlight the cyclic behavior of the strain variation during reducing CO oxidation in both NPs. Given the faceted character of the NPs, the initial surface strain state is anisotropic and strongly correlated to the facet type (Tables S5, S6  . A similar initial surface strain state is observed in NP650, highlighting the strong correlation between facet type and initial strain state, which is very well captured by MS simulations (see Figure 4). The introduction of 2.5% O 2 in the gas mixture induces very distinct and reproducible strain variations in NP300 (see Fig. S16 and Table S6) and NP650 (see Fig. S17 and Table S7). The strain evolution is strongly correlated to the facet type and to the initial strain state. As shown in Fig. S16b and Table S6, a relaxation of the compressive strain is observed in the {111} facets, (∆ 111 111 = 0.93x10 −4 and 0.63x10 −4 for the first and second cycle, respectively). On average the {111} facets become strain free in Ar + 2.5% O 2 atmosphere (Table S6) (Table S7). In contrast, the opposite trend is observed during CO oxidation in CO excess (χ = 10), where most of the facets come back to their initial strain state. An increase of the tensile strain is therefore observed for the {100}, {113}, {113} and {110} families, while the {111} facets resume their initial compressive strain state during the 1 st but not during the 2 nd cycle, where a slight tensile strain builds up. Overall, an increase of the magnitude of the surface strain either tensile or compressive is observed for all but one facet families during reducing CO oxidation. This cyclic behavior consisting of a strain relaxation during O 2 exposure and a strain increase during non stoichiometric CO oxidation is well illustrated in Fig. S16. Although less pronounced than in NP300, it is also observed in NP650, not only in non stoichiometric conditions, but also during the subsequent stoichiometric cycle (see Fig. S17). Moreover, Figure S16 also reveals that facets belonging to the same family tend to have a very consistent behavior. This is particularly striking for the {100} (Fig. S16a), {111} (Fig. S16b) and {113} (Fig. S16e) facet families. Interestingly, this is not the case for the {110} type facets, which exhibit an heterogeneous behavior during the reducing CO oxidation cycles (Fig. S16b). This also explains why on average the cyclic behavior is not observed for this facet type (Fig. 5a). For NP650, with the exception of the {113}, where all the facets experience a very similar strain evolution (Fig. S17e), the behavior of individual facets tend to be less homogeneous. This is reflected by the smaller amplitude of the oscillations during the gas cycles, in particular for the {100} and the {113} families (see Fig. 5b).    To allow a quantitative comparison, the atomic resolved strain values were averaged over the experimental voxel size (6.7 nm). Since the atomic relaxation is mostly perpendicular to the facets, the α angle between the facet normal and the scattering vector q 111 has to be taken into account for the calculation of the theoretical average strain in the side {100} and {11 1} facets: ∆ 111 c 100 = ∆ 111 100 ×cos 2 α. Note that as illustrated in Fig. 4, the strain field strongly depends on the NP shape and boundary conditions, which results in large atomic displacements not only perpendicular to the facets but also parallel to the facets (for instance for the {113} facets). These displacements can not be captured by the DFT calculations, which could contribute to explain the discrepancy between the experimental values and the DFT results. The results displayed in Table S8 suggest a low coverage on the {111} and {111} facets (between 0.125 and 0.25 ML) during oxygen exposure in Ar + 2.5% O 2 atmosphere. In contrast a high coverage is expected on the {100} facet (between 0.75 and 1 ML). The DFT calculations therefore confirm that adsorption occurs preferentially on low coordinated facets that are initially in tension, in good agreement with the d-band model.   If the facet dependent character is mostly retained during stoichiometric CO oxidation in NP650, this is not the case for NP300. This is illustrated in Fig. S18 showing that individual facets belonging to the same family do not follow the same trend during stoichiometric CO oxidation. For instance, two of the facets belonging to the {111} family experience a tensile strain (the [111] and [111]), while the remaining four go into compression (see Fig. S18a). Similar observations can be drawn for the remaining families. At odds with previous works on single crystal surfaces and with the trends observed in reducing CO oxidation conditions, the analysis of the average strain evolution reveals that the strain evolution is weakly correlated to the facet type during stoichiometric CO oxidation: facets can go into tension or compression independently on their crystallographic orientation. In contrast, facets localised in the same region of the nanocrystal tend to exhibit a more similar behavior (Fig. S19). This is particularly true for the facets localised in the regions labeled ZX and -YZ, which go into compression (Fig. S19a) and tension (Fig. S19b), respectively. For the sake of comparison, the strain evolution in the four regions (ZX, -ZX, YZ and -YZ) is shown during the reducing CO oxidation cycles (Fig. S20). In these conditions, the strain variations are strongly correlated to the facet type, and therefore facets belonging to the different regions, with different surface termination exhibit a very heterogeneous behavior. This further highlights the existence of two regimes in NP300. A facet dependent regime in reducing CO oxidation conditions, where the strain evolution depends on the facet type and a localised regime in stoichiometric conditions, where the strain evolution is predominantly controlled by the facet position in the NP. The strain variations remain mostly independent of the facet type during the subsequent O 2 exposure (Ar + 12.5% O 2 , 4 th cycle). As illustrated in Fig. S18, facets that experienced compressive (tensile) strain during stoichiometric CO oxidation go into tension (compression) in O 2 atmosphere, independently of their type. On the other hand, the localised character of the strain variations is retained during O 2 exposure: the ZX and -ZX regions that experienced a compressive strain during CO oxidation go into tension in O 2 atmosphere, while the opposite trend is observed for the neighboring YZ and -YZ regions. This allows to relax most of the large surface strain that was induced by the stoichiometric oxidation. Interestingly and as illustrated in Figs. S18 and S19, this surface strain relaxation is initiated before the O 2 exposure, as illustrated by the overall decrease of ∆ 111 during the Ar + 25% CO and Ar exposures preceding the O 2 exposure. This overall decrease of the average strain per facet is consistent with the decrease of both the microstrain (Fig. 3a) and strain field energy (Fig. 3c), which starts rapidly after the end of the stoichiometric CO oxidation. This relaxation is also accompanied by a decrease of the extent of the compressive regions at the NP / substrate interface (Fig. S8h-j), suggesting that a reorganisation of the interfacial dislocation network can also contribute to accommodate the large strain induced during the gas reaction.        Figure S23 and Table S10 show the variation of the surface lattice displacement for facets located at the top and bottom of NP300 during stoichiometric CO oxidation. The displacement variations for the facets located at the bottom of the NP are significantly larger than the variations on the top facets. Large strain/displacement variations are characteristic of high activity regimes as suggested by Plodinec et al. [6], which would suggest that preferential sites for CO 2 formation are predominantly located on the facets located close to the interface. This indicates that the thermoelastic strain induced during the cooling of the NP at the substrate/NP interface can affect the reactivity and confirms the importance of metal-support interaction to improve performance in catalysis.  Figure S24 displays the CO conversion into CO 2 as a function in reducing, stoechiometric and oxidizing conditions. Note that the measurements were carried out on a different sample with a similar size distribution of Pt NPs.  Figure S25 shows the evolution of the surface lattice displacement during the two non stoichiometric cycles and the stoichiometric cycle in NP300. A large and inhomogeneous surface displacement builds up during stoichiometric CO oxidation, in good agreement with the increase of the microstrain (Fig. 2a) and strain-field energy (Fig. 2c). The strain relaxation is initiated during the subsequent 25% CO and Ar exposure, most likely through a reorganisation of the interfacial dislocation network. With the introduction of 12.5% O 2 , the FWHM of the histogram almost completely comes back to is initial value, suggesting that these oxidative conditions allow to oxidize the remaining CO adsorbates on the surface step sites.