Three-dimensional strain dynamics govern the hysteresis in heterogeneous catalysis

The study investigates how three-dimensional strain dynamics in single gold nanocrystals influence catalytic behavior and hysteresis during CO oxidation. Surface lattice strain is known to modulate adsorption and reaction energetics via d-band center shifts, particularly in late transition metals such as Au. Prior theory shows tensile strain enhances O2 adsorption and lowers CO2 formation barriers on Au surfaces. In nanoparticles, strain arises from intrinsic factors (size, morphology, facets, defects) and extrinsic factors (support interfaces, core–shell). Conventional X-ray diffraction provides averaged strain, and environmental TEM offers 2D/limited 3D structural dynamics; however, operando three-dimensional strain mapping has been lacking. The authors design a morphology-controlled Au system (cuboctahedra vs cubes ≈60–70 nm) to tune intrinsic strain and use operando Bragg coherent diffraction imaging (BraggCDI) to map site-specific 3D strain under CO oxidation. The central hypothesis is that anisotropic, facet-dependent strain dynamics govern active site formation and the observed normal/inverse hysteresis in catalytic performance, and that elastic energy landscapes at the single-particle level differ between heating and cooling cycles.

Background covers the d-band model linking lattice strain to catalytic activity on metal surfaces and DFT studies showing tensile strain enhances O2 adsorption and facilitates CO2 formation on Au. Sources of nanoparticle strain include morphology, facets, defects, and support interactions. Environmental TEM has visualized structural changes of catalysts under reaction (e.g., oscillatory behavior of Pt NPs during CO oxidation), but lacks full 3D strain information. Bragg coherent diffraction imaging (BraggCDI) enables in situ 3D mapping of displacement/strain and defects and has been applied to localize active sites and follow dynamics in various catalytic and materials systems. The authors’ prior work showed dynamic faceting and nanotwin networks in Au during CO oxidation. The current study builds on these to directly link 3D strain dynamics with catalytic hysteresis in morphology-controlled Au nanocrystals.

• Materials synthesis and characterization: TiO2 support prepared by sol–gel (Ti(OPr)4 in isopropanol, hydrolyzed at −3 °C; gelation at RT; drying 50 °C; calcination 450 °C). Au nanoparticles synthesized via two-step seed-mediated growth (Sau & Murphy method): seeds (HAuCl4 + CTAB, reduced by NaBH4) produced ~6.0 ± 0.7 nm Au; cubes grown with higher ascorbic acid (0.9 mL, 0.1 M) and cuboctahedra with lower (0.45 mL). Au NPs supported on TiO2 (1 wt% Au), acidified to pH ~1, washed, dried (110 °C), calcined (200 °C 1 h then 400 °C 1 h) to remove CTAB. Morphologies and size distributions (cuboctahedra 68.0 ± 8.0 nm; cubes 63.5 ± 6.5 nm) confirmed by SEM/STEM and SAXS.
• Catalytic testing: Tubular reactor with 10 mg catalyst diluted in 90 mg quartz; CO:O2 = 0.4:4.0% in He, total flow 100 mL/min; heating ramp 3 °C/min to isothermal conditions; gases analyzed by GC-TCD. CO conversion measured vs temperature, capturing hysteresis during heating (light-off) and cooling (light-out).
• Bragg coherent X-ray diffraction imaging (operando): Measurements at APS 34-ID-C. Catalyst powder drop-cast on Si wafer in operando reactor. Incident X-rays 9 keV; focused coherent beam ~600 × 600 nm^2; (111) Bragg condition collected on Timepix detector (55 µm pixels) at 430 mm. 3D coherent diffraction acquired as rocking curves (0.02° step, 41 frames × 10 s, 2–5 repetitions) for the same NP across reaction conditions: RT, 100, 200, 300, 400 °C during heating and cooling. Gas during BraggCDI: CO/O2 mixture (0.4:4%) at 20 mL/min; effluent simultaneously monitored by mass spectrometry. Phase retrieval with iterative algorithms to reconstruct 3D electron density (amplitude) and displacement field u111 (phase) with picometer lattice displacement sensitivity and ~15 nm real-space resolution. Strain along [111] obtained by spatial differentiation (∇u111) with sensitivity ~2 × 10^−4. Only the 111 strain component is measured due to single reflection constraints in the operando cell; it remains sensitive to distortions associated with other facets. Statistical strain distributions computed for surface vs interior regions. Elastic strain energy estimated using E = (K/2) ∫(u111/x111)^2 dV, with K being Au bulk modulus, mapping energy at attojoule scale across conditions.

• Morphology-dependent initial strain: After calcination (400 °C), both morphologies exhibit compressive surface strain; mean surface strain magnitude differs by an order of magnitude: cuboctahedron −7.83 × 10^−5 vs cube −3.52 × 10^−4 along [111]. Strain is most pronounced at edges {110} and corners {111} for cubes.
• Catalytic hysteresis behavior: CO oxidation shows distinct hysteresis loops by morphology—cuboctahedra exhibit inverse hysteresis (higher conversion on heating), cubes exhibit normal hysteresis (higher conversion on cooling).
• Operando 3D strain dynamics (cuboctahedron, AuNP1): Upon CO/O2 flow, surface strain switches from compressive to tensile (from −7.83 × 10^−5 to +1.40 × 10^−5 mean). Tensile strain initially localizes on {111} facets and expands with temperature; at 200 °C tensile regions connect across opposite {111} facets. At 400 °C (near maximum CO conversion), a tensile-strained ‘corona’ forms around the particle (strain > +1.0 × 10^−4), counterbalanced by compressive regions (strain < −1.3 × 10^−4). During cooling, anisotropic patterns recur but are temperature-shifted (e.g., 300 °C cooling ≈ 200 °C heating), mirroring the inverse hysteresis in activity. Tensile regions extend from surface into interior during reaction and recede after.
• Operando 3D strain dynamics (cube, AuNP2): Tensile strain concentrates primarily at {110} edges and {100} facets, less at {111} corners, aligning with DFT predictions of higher reactivity for {100}/{110} vs {111}. At 400 °C, only four of six {100} facets exhibit strong tensile strain (active sites), while two remain compressive, demonstrating unequal reactivity among identical facets. Facet-resolved strain histograms quantify these differences. Small, largely reversible displacement/volume changes observed across the loop (indicative values from representative sequence: RT ≈ V0; 300 °C ≈ 99% V0; 400 °C ≈ 98% V0; cooling 300 °C ≈ 99% V0; RT back ≈ 101% V0).
• Elastic energy landscape: Energy mapping at attojoule resolution shows single-particle hysteresis in elastic energy. For the cuboctahedron, the RT elastic energy and strain pattern after a full CO oxidation cycle do not return to the initial state, indicating irreversible elastic energy losses (lattice deformation and exothermic heat dissipation), consistent with inverse hysteresis. For the cube, the strain energy is essentially unchanged through the cycle, and the RT state recovers the initial pattern/energy, consistent with normal hysteresis and a higher pre-strained state that resists further deformation.
• Active site identification via tensile strain: Tensile-strained regions correlate with increased catalytic activity (per d-band model), enabling direct 3D localization of active sites under operando conditions.

The findings directly link 3D anisotropic strain dynamics to catalytic hysteresis in CO oxidation at the single-nanoparticle level. Tensile strain narrows the d-band, increases occupancy, and modifies adsorption/dissociation energetics; thus, the observed tensile regions on specific facets, edges, and corners identify active sites. In cuboctahedra, the growth and inward propagation of tensile strain during heating correlate with rising conversion, while temperature-shifted recurrence during cooling explains inverse hysteresis and points to path-dependent elastic responses. The lack of full recovery in elastic energy after a cycle evidences irreversible deformation and heat dissipation as contributors to inverse hysteresis. In cubes, pre-existing higher compressive surface strain appears to buffer further deformation, leading to recovery of the initial elastic state and normal hysteresis. The discovery that identical crystallographic facets can display unequal strain and thus unequal reactivity highlights the role of local strain heterogeneity beyond facet identity. Mapping elastic energy landscapes with attojoule sensitivity reveals that catalytic performance hysteresis is encoded in the nanoparticle’s elastic state, not solely in external reaction conditions. These insights underscore the need to engineer and control strain states to modulate activity and hysteresis in heterogeneous catalysis.

Operando BraggCDI provided 3D, site-specific strain maps of single, morphology-controlled Au nanocrystals during CO oxidation, revealing anisotropic strain formation/propagation, facet- and edge-specific tensile regions that serve as active sites, and unequal reactivity among nominally identical facets. The work demonstrates that catalytic hysteresis (normal vs inverse) originates at the single-particle level through differences in elastic energy evolution: cubes largely recover their initial elastic state, while cuboctahedra exhibit irreversible elastic energy changes. Mapping the elastic energy landscape at attojoule resolution establishes a direct structural–energetic–reactivity link. These results suggest that intentionally manipulating the elastic energy/strain distribution could tune catalytic performance and hysteresis, and that operando 3D strain imaging can inform the design of stable, efficient catalysts and studies of deactivation processes. Future research may extend to measuring full strain tensors via multiple reflections, exploring different supports/morphologies, and implementing strategies to control strain to optimize activity and minimize hysteresis-related losses.

• Strain characterization used only the (111) Bragg reflection; thus only the [111]-projected displacement/strain component was measured. Full strain tensor determination would require multiple non-parallel reflections, which was not feasible in the operando setup.
• Single-particle operando measurements focused on representative nanocrystals (e.g., one cuboctahedron, one cube), which may limit statistical generalizability across populations.
• The Au nanoparticles (~60–70 nm) are larger than the size range typically associated with highest Au catalytic activity, requiring elevated temperatures to observe activity; conclusions at lower temperatures or for smaller particles may differ.
• Gas composition and flow differ between bulk catalytic tests (100 mL/min in He balance) and operando BraggCDI (20 mL/min), potentially influencing kinetics; however, qualitative hysteresis–strain correlations were maintained.
• Surface strain maps are projections along [111] and sensitive to reconstruction artifacts inherent to phase retrieval; although displacement resolution is picometer-level and strain sensitivity ~2 × 10^−4, absolute values of local extremes should be interpreted considering these limits.