Deciphering the structure of heterogeneous catalysts across scales using pair distribution function analysis

Pair distribution function (PDF) analysis has become an important tool for the characterization of heterogeneous catalysts due to its ability to provide structural information across different length scales (local atomic environment to long-range structure). As opposed to conventional diffraction methods, PDF does not require long-range order, making it ideal for the study of catalysts comprising disordered phases, including defect-rich small nanoparticles or amorphous phases. Static (correlated) disorder in the PDF is visualized as deviations of the local from the average structure, making it a powerful tool to study crystal defects. As heterogeneous catalysts are complex (multicomponent, multiphasic) materials, a differential PDF approach allows the identification of contributions from different phases. Heterogeneous catalysts are complex materials, often containing multiple atomic species and phases with various degrees of structural order. The identification of structure–performance relationships that rely on the availability of advanced structural characterization tools is key for rational catalyst design. Structural descriptors in catalysts can be defined over different length scales from several angstroms up to several nanometers (crystalline structure), requiring structural characterization techniques covering these different length scales. Pair distribution function (PDF) analysis is a powerful method to extract structural information spanning from the atomic to the nanoscale under in situ or operando conditions. We discuss recent advances using PDF to provide insight into the atomic-to-nanoscale structure of heterogeneous catalysts. Heterogeneous catalysts are complex materials, often containing multiple atomic species and phases with various degrees of structural order. The identification of structure–performance relationships that rely on the availability of advanced structural characterization tools is key for rational catalyst design. Structural descriptors in catalysts can be defined over different length scales from several angstroms up to several nanometers (crystalline structure), requiring structural characterization techniques covering these different length scales. Pair distribution function (PDF) analysis is a powerful method to extract structural information spanning from the atomic to the nanoscale under in situ or operando conditions. We discuss recent advances using PDF to provide insight into the atomic-to-nanoscale structure of heterogeneous catalysts. a measure of the scattering amplitude of a wave by an isolated atom. characterized by a phase relationship between the incident and scattered (X-ray, neutron, electron) beams. all deviations from the ideal crystal. These can be classified according to their dimensionality as point (e.g., Frenkel defect, vacancy), line (e.g., dislocation), and planar (e.g., stacking fault) defects. contains information on the static and dynamic (due to the movement of atoms) local structure. It extends over a wide range of Q and is weaker than coherent scattering; therefore, it is more challenging to measure than Bragg peaks. Elastic and inelastic diffuse scattering together with the Bragg peaks constitute the total scattering intensity. experiment in which a material property (e.g., its structure, surface chemistry, or composition) is probed over time under specific conditions (e.g., elevated temperature, gas or liquid flow). the difference between the incident wave vector k0 and the scattered wave vector k1 in a scattering experiment, Q = k0 − k1. The magnitude of Q is defined in Equation 1. refers to a specific case of an in situ study where the catalyst is exposed to reaction conditions while the products and reactants are simultaneously analyzed and quantified. a type of planar crystal defect describing the nonideal stacking of layers of atoms. Turbostratic stacking faults are a type of stacking fault where the layers are randomly rotated or translated relative to each other. the equivalent of the PDF in reciprocal space. It represents the normalized, coherently scattered intensity from the sample. derived from the unit cell of a crystal, for example, by its expansion along one or multiple unit cell vectors. The symmetry of the supercell is always lower than that of the parent unit cell. Repeating the supercell in space often allows a better description of the structure of defect-rich crystals compared with the parent unit cell. describes the agreement between the observed (Gobs) and calculated (Gcalc) PDF, which is defined asRw=∑i=1Nwri∣Gobsri)−Gcalcri)2∑i=1NwriGobs2ri[I] Here, the N points of the observed PDF are weighted by their respective uncertainties wi. A perfect fit between a model structure and the acquired data gives Rw = 0.