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Measuring local polar ordering is key to understanding ferroelectricity in thin films, especially for systems with small domains or significant disorder. Scanning nanobeam electron diffraction (NBED) provides an effective local probe of lattice parameters, local fields, polarization directions, and charge densities, which can be analyzed using a relatively low beam dose over large fields of view. However, quantitatively extracting the magnitudes and directions of polarization vectors from NBED remains challenging. Here, we use a cepstral approach, similar to a pair distribution function, to determine local polar displacements that drive ferroelectricity from NBED patterns. Because polar distortions generate asymmetry in the diffraction pattern intensity, we can efficiently recover the underlying displacements from the imaginary part of the cepstrum transform. We investigate the limits of this technique using analytical and simulated data and give experimental examples, achieving the order of 1.1 pm precision and mapping of polar displacements with nanometer resolution.

 

Defects may display high reactivity because the specific arrangement of atoms differs from crystalline surfaces. We demonstrate that high-temperature steam pretreatment of palladium catalysts provides a 12-fold increase in the mass-specific reaction rate for carbon-hydrogen (C–H) activation in methane oxidation compared with conventional pretreatments. Through a combination of experimental and theoretical methods, we demonstrate that an increase in the grain boundary density through crystal twinning is achieved during the steam pretreatment and oxidation and is responsible for the increased reactivity. The grain boundaries are highly stable during reaction and show specific rates at least two orders of magnitude higher than other sites on the palladium on alumina (Pd/Al 2 O 3 ) catalysts. Theoretical calculations show that strain introduced by the defective structure can enhance C–H bond activation. Introduction of grain boundaries through laser ablation led to further rate increases.