Vibrational Disorder Effects on Temperature-Resolved X-Ray Absorption Signatures of Metal Catalysts: From Single-Atoms to Clusters and Nanoparticles.

Revealing dynamic local-structure changes of (sub)nanometric metal species under operating conditions is essential. In heterogeneous catalysis, this insight enables the rationalization of operation and optimization of catalyst efficiency and stability. Extended X-ray absorption fine structure (EXAFS) provides element-specific access to metal-metal coordination numbers, interatomic distances, and local disorder, which is pivotal when active motifs lack long-range order. Yet, accurate determination of structural parameters from EXAFS signatures is often complicated by the convolution of static heterogeneity and thermal vibration effects, encoded in the Debye-Waller factor: σ2=σdynamic2(T)+σstatic2. This coupling, especially at elevated temperatures typical of in situ and operando studies, obscures genuine structural changes. Here we present a temperature-resolved EXAFS study geared toward deconvoluting σdynamic2(T) in three supported Ag catalysts spanning different σstatic2 levels and metal aggregation states: Al2O3-supported Ag nanocrystals, few-atom Ag clusters confined to a zeotype host, and single-atom Ag dispersed on WOx/Al2O3. Over 298-723 K, representative of catalyst activation and deployment conditions, we observe a nuclearity-dependent vibrational stiffness: Ag-Ag bonds in nanoparticles show strong thermal disorder, whereas Ag-O bonds in single-atoms and confined clusters remain comparatively rigid, limiting dynamic fluxionality. While a classical formalism, such as the correlated Einstein model, adequately captures nanocrystal dynamics, it fails for few- and single-atom motifs. Therefore, a direct parametrization of σ2(T) is proposed, better capturing vibrational disorder in low-nuclearity metal catalysts. The results provide guidance for decoupling thermal and static contributions in temperature-resolved EXAFS studies, enabling a more reliable structural analysis of (sub)nanometric metal species under operando conditions.