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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.

We communicate a feasibility study for high‐resolution structural characterization of biomacromolecules in aqueous solution from X‐ray scattering experiments measured over a range of scattering vectors (q) that is approximately two orders of magnitude wider than used previously for such systems. Scattering data with such an extendedq‐range enables the recovery of the underlying real‐space atomic pair distribution function, which facilitates structure determination. We demonstrate the potential of this method for biomacromolecules using several types of cyclodextrins (CD) as model systems. We successfully identified deviations of the tilting angles for the glycosidic units in CDs in aqueous solutions relative to their values in the crystalline forms of these molecules. Such level of structural detail is inaccessible from standard small angle scattering measurements. Our results call for further exploration of ultra‐wide‐angle X‐ray scattering measurements for biomacromolecules.