Measuring Polar Displacement and Lattice Strain in Ferroelastic Specimens via Precession-Enhanced Cepstral Analysis

Understanding local crystallography – including local lattice parameters, interatomic spacings, and polarity – is key to understanding ferroelectricity, especially in systems with small domains, significant disorder, or interfacial features. Scanning nanobeam electron diffraction (NBED) combined with new high-speed, pixelated scanning transmission electron microscopy (STEM) detectors make it possible to measure a diffraction pattern (kx, ky) at every scan position (x, y). This opens doors to investigate crystalline properties such as lattice parameters, local fields, polarization directions, and charge densities with relatively low beam dose over large fields of view. However, extracting these signals of interest from confounding signals such as thickness or crystallographic mistilt effects remains challenging. Here, we combine a cepstral approach, which is similar to a 2D pair-correlation function, with precession electron diffraction (PED) to measure local polar displacements in non-centrosymmetric materials while suppressing artifacts from dynamical or mistilt effects. We first apply these techniques to a reference sample of GaN and demonstrate that the addition of PED reduces the standard deviation of the lattice parameter measurement 0.56 pm to 0.32 pm. We also measure the length of the vector associated with the non-centrosymmetric nature of the unit cell, and see that its standard deviation is reduced from 3.5 pm to 1.9 pm. Computational work shows that adding precession also increases the robustness of these measurements to specimen mistilt. We then apply these techniques to study polar domains in a sample of PMN-PT, and observe domains on the 100 nm length scale.