# Three-dimensional strain dynamics govern the hysteresis in heterogeneous catalysis

Sep 18, 2020

### Morphologies of gold nanocrystals

Because of the different amount of reductive agent used in our experiment, a colloidal-based seed-mediated growth method based on the work of Sau et al.25, we can control and tune the morphology of the Au nanocrystals. The gold seeds are formed in the presence of a surfactant leading to spherical nanoparticles with monodisperse size distribution of 6.0 ± 0.7 nm. Gold cuboctahedron-shaped nanocrystals and nanocubes were then grown by addition of an appropriate quantity of seed solution to the aqueous growth solutions containing different concentrations of ascorbic acid enabling to control the degree of edges and corners truncation. The gold nanocrystals were then deposited by impregnation on TiO2 support and dried under air. Figure 1a shows scanning electron microscopy (SEM) images of the supported gold nanocrystals. The detailed synthesis procedures are described in ‘Methods’. The cuboctahedron and cube nanocrystals display monodisperse size distributions of 68.0 ± 8.0 nm and 63.5 ± 6.5 nm, respectively, determined by scanning electron microscopy and small angle X-ray scattering measurements (Supplementary Fig. 1). The nanocube crystals are composed of six {100} facets, the edges are truncated to {110} planes, and the corners are formed by small {111} facets. The cuboctahedron crystals are truncated cubes with higher ratio of {111} to {100} facets.

### Local lattice distortion variations in supported Au NPs

3D lattice displacement maps were obtained from BraggCDI measurements. The pristine supported gold nanocrystals were first imaged in air. In brief, coherent X-ray diffraction patterns were collected around the gold (111) Bragg peak at 9 keV at the 34-ID-C beamline (Advanced Photon Source, USA). The 3D diffraction pattern obtained by rocking scans around the (111) Bragg peak of the cube is presented in Fig. 1b. Using iterative phase retrieval algorithms, the 3D Bragg electron density and the lattice displacement field of the nanocrystals are determined. The detailed coherent X-ray diffraction data analysis is described in the ‘Methods’. The amplitude of the reconstructed image represents the electron density and the phase corresponds to the projection of the displacement of the crystal lattice on the scattering vector q111. The lattice displacement resolution reaches the picometre level, while the real space resolution 15 nm.

The 3D lattice displacements maps of the cuboctahedron and cube nanocrystals are displayed in Fig. 1c. The nanocrystals were capped with CTAB molecules. The residual distortion in the displacement field observed at the surface for the as-synthetised nanocrystals arises from the growth conditions which are far from equilibrium26 as shown in Fig. 1c. The size-limiting effect of CTAB affects the growth rate and the lattice deformations across the nanocrystal, from the centre to the outside regions. These inhomogeneities are best visualised in the cross-sections views of the lattice displacement maps shown in Fig. 1d. The images are coloured by the local displacement field where red (positive sign) indicates the projected displacements along the [111] direction, u111, and blue (negative sign) implies the opposite direction. The maximum u111 value is ~10 and 20 pm of the Au111 lattice constant for the cuboctahedron and the cube, respectively. Figure 1d shows that the stress induced by the capped CTAB molecules on gold has a different impact on the flat facets compared to the curved regions of the crystal surface.

Strain along the [111] direction was determined by spatial differentiation of the lattice displacement field27u111/∂x111, the 3D strain maps of the nanocrystals are resolved and shown in Supplementary Fig. 2. The 3D strain images enable to visualise and quantify the bulk and surface strains in the NPs, showing strain that can be compressive or tensile. The strain sensitivity is of the order of ~2 × 10−4 due to the strong sensitivity of X-rays to the crystal lattice spacing. Such a strain sensitivity is nowadays routinely achieved using BraggCDI methods as reported by28,29,30,31. It is most pronounced at edges {110} and corner sites {111}, in the case of the gold cube. These 3D strain maps clearly reveal the anisotropic strain distribution of both nanocrystals at room temperature (RT), and a mean surface strain that is compressive for the as-prepared dried cube and tensile for the cuboctahedron. Upon calcination at 400 °C and removal of the CTAB molecules, both nanocrystals display a compressive surface strain, as expected for tensile surface stress of metals32,33. Only the map of the [111] component of the lattice strain tensor is presented. Indeed, to determine the full strain tensor, at least three or more non-parallel reflections must be collected. Multiple reflections from a single particle have been measured previously using BraggCDI29,31,34 but such a study could not be carried out in this work due to the in situ experimental limitations of the operando cell. However, the 111 component is also sensitive to 100, 110 latice distortions, and so used throughout as a signature of the phenomenon occurring at the surface of the nanocrystal during the catalytic process, to image their elastic response35. The projected strain measurements are quantitatively summarised in histograms, in Fig. 2, for the two calcined nanocrystals. The histograms compare the strain distribution from the inner regions (blue) of the NPs to that of their surfaces (red). As anticipated, the cuboctahedron crystal exhibits the lowest strain structure, with a mean compressive surface strain value of −7.83 × 10−5, while the cube crystal mean surface strain value rises up to −3.52 × 10−4. This demonstrate that the strain range of the NPs spans over an order of magnitude depending solely on the nanocrystal morphology.

### Effects of strain on reaction kinetics

To further study the impact of strain in nanoparticles on their catalytic properties, we performed operando BraggCDI measurements during the CO oxidation reaction. The gold nanocrystals in our study are larger than optimum size range where gold is considered to be catalytically active. Nonetheless, they do present catalytic activity at high temperature as shown in Fig. 3 presenting the CO conversion as function of temperature of the cuboctahedra and cubes nanocrystals. We observe typical temperature hysteresis loops, characteristic of the CO oxidation reaction. However, both gold morphologies present distinct hysteresis loops: inverse and normal hysteresis, respectively. For a normal hysteresis, the conversion of CO into CO2 is higher during the cooling step (light-out curve), while for the inverse hysteresis, the conversion of CO is higher during the heating step (light-off curve). The latter results evidence the impact of the nanocrystal morphology and their strain distribution on the hysteresis profile and their catalytic properties.

We further demonstrate that the hysteresis loops correlate with the nanocrystals surface strain dynamics. The detailed experimental conditions regarding gas environment of the operando BraggCDI measurements are described in ‘Methods’. Figure 4a, b presents the 3D images and cross-sectional images from the BraggCDI patterns of the gold cuboctahedron (AuNP1). The dashed plane represents the location of the cross-section. We observe a mean surface compressive to tensile strain swap (from −7.83 × 10−5 to 1.40 × 10−5) upon flowing the CO/O2 gas mixture on the gold nanocrystal surface, in agreement with Suzana et al.12.

The changes of the compressive (blue) and tensile (red) strains are shown at the different steps of the reaction. We observe an initial tensile strain located on the {111} facets, which expands as the temperature rises. At 200 °C, the tensile strain propagates across the nanocrystal, and enlarges through the connection of the opposite {111} facets. This is best visualised in Fig. 4a, which displays the 3D highly compressive and tensile strain evolutions of the nanoparticle during the CO oxidation reaction. We notice the formation of a tensile-strained corona (>1.0 × 10−4, in red) around the nanocrystal counterbalanced by two compressive strained regions (<−1.3 × 10−4, in blue). The tensile strain keeps building up until 400 °C, when the maximum CO conversion is attained. It is well established that the lattice strain can change the reactivity of metal surfaces1,2,3. This is explained by the d-band model, where the tensile strain (regardless of direction in the lattice) leads to a narrowing of the d-band and an increased population of the latter, for late transition metals. The altered d-band centre affects the adsorption and dissociation energies. Accordingly, the tensile strain areas indicate the localisation of the active sites during catalytic CO oxidation reaction.

These tensile-strained areas from the surface extend to inside the nanocrystal during the catalytic process, and revert after the reaction is complete (Fig. 4). During the cooling process, the tensile strain is effectively released and exhibits similar anisotropic strain patterns as during the heating process. Surprisingly, the surface strain patterns are temperature-offset between the heating and the cooling processes coinciding with the hysteresis behaviour of the nanocrystal. As clearly shown in Fig. 4b, the inner strain pattern at 300 °C during cooling matches the one at 200 °C during heating, the 200 °C cooling pattern is equivalent to the 100 °C heating one, and finally the 100 °C and RT cooling present the similar four-fold pattern of the 100 °C heating, as expected for an inverse hysteresis loop. This is quantitatively summarised in the strain histograms in Supplementary Fig. 3, comparing the strain distribution from the inner regions to the surface strain distribution of the cuboctahedron. The strain histograms emphasise the occurrence of highly tensile-strained surface regions at 400 °C and further confirm the inverse hysteresis behaviour.

We also imaged a gold cube (AuNP2) under operando CO oxidation reaction (Fig. 5). During the heating process, under reactive conditions, we also observe the formation of highly surface strained regions, which peak at 400 °C, corresponding to the highest CO conversion. Similarly to the cuboctahedron, the cube surface strain dynamics present a hysteresis behaviour, coinciding with the CO2 production. The evolution of the surface strain dynamics is displayed in Fig. 5 demonstrating the normal hysteresis behaviour of the cube (Fig. 3b). The largest tensile strain values are primarily concentrated at the {110} edges and {100} facets and less pronounced at the {111} corners. This is in good agreement with DFT calculations for faceted gold nanoparticles showing that the {100} and {110} are the more reactive for oxidation reaction than the {111} which have higher coordination numbers8.

Outstandingly, the tensile strain at 400 °C, pointing to the active sites, is restricted to four of the six {100} facets of the cube, the remaining two show a compressive strain (Fig. 5c). Although facet-dependent reactivity is well-known, this is the first proof of unequal reactivity of identical facets in a single nanocrystal. This is quantitatively summarised in the strain histograms in Fig. 5d, comparing the surface strain distributions of the six {100} facets.

### Elastic energy landscape

To elucidate the mechanism driving the hysteresis response of the cuboctahedron and the cube, we determine the elastic energy landscape using the three-dimensional strain distribution to assess the elastic energy which is defined as (Eq. (1)):

$$E_{mathrm{S}} = frac{3}{2}K,{int} {left( {frac{{partial u_{111}}}{{partial x_{111}}}} right)^2dV}$$

(1)

where K is the bulk modulus of Au, u111 is the displacement value along [111], and x111 is the (111) lattice constant of Au. The strain induced by the deviations of atoms from their equilibrium position are accounted by the elastic strain energy, irrespective of the original cause of displacement. Figure 6 shows the values of the elastic energy, on the order of attojoules, at different reaction conditions.

The 3D mapping of the energy landscape unveils the dynamics of AuNP1 showing a distinct behaviour in strain energy between the heating and cooling steps of the CO oxidation reaction. Although the hysteresis behaviour during oxidation reaction is expected from a macroscopic point of view (catalytic conversion)36, it turns out to be at the single-particle level. This is surprising and could be explained by taking into account losses in the form of irreversible elastic energy release via lattice deformation and heat dissipation due to the exothermicity of the reaction. This is further supported by the value of the elastic energy of AuNP1 at RT after a CO oxidation cycle which shows that the nanocrystal does recover neither its strain energy (green symbol in Fig. 6) nor its initial strain pattern (Fig. 4). This is clear indication of losses in the form of irreversible elastic energy and explanation to the inverse hysteresis behaviour. On the other hand, the cube nanocrystal shows no variation of strain energy during the catalytic reaction, recovering its initial strain pattern and energy at RT after a cycle. This is compatible with a normal hysteresis behaviour where the pre-strained state of the cube (an order of magnitude higher than that of the cuboctahedron at RT) prevents from deformation and thus energy losses.

In conclusion, using operando BraggCDI, we studied at the single-particle level, the strain dynamics of morphology-controlled gold nanocrystals during the CO oxidation reaction. We revealed their anisotropic strain formation and propagation, and experimentally unveiled that identically crystallographic oriented facets in a single nanocrystal can be differently affected by strain leading to “identical-facet”-dependent reactivity. This anisotropic strain may also provide an explanation for shape modifications during CO oxidation reaction37. Finally, we followed the evolution of the elastic energy landscape with attojoule energy resolution and found out that the catalytic hysteresis is occurring at the single-particle level. We discovered the origin of the hysteresis and demonstrated that it is linked to the structural properties and strain dynamics of the catalysts and not only to the variations of reaction conditions as long believed. This suggests that finding ways to manipulate the elastic energy is of paramount importance for tuning the chemical and catalytic properties of nanomaterials.