Displacement separation analysis from atomic-resolution images

Structural distortions frequently occur in materials, either periodically (ferroelectric or antiferroelectric) or in local areas (domain boundaries, surfaces/interfaces, dislocations). Measuring atomic displacements from an average lattice is of crucial importance for analyzing structural distortions and their connections to physical properties. Conventionally, the displacements are measured atom-by-atom by fitting atomic-resolution images with two-dimensional gaussian functions. Here, we exhibit an efficient method, named Displacement Separation Analysis, DSA in short, to directly separate atomic displacements from an average lattice based on Fourier space filtering. Using antiferroelectric AgNbO₃ as a model system, we demonstrate the consistence between DSA and gaussian fitting. The suppression of polarization at interfacial region of h-LuFeO₃/α-Al₂O₃ heterostructure and the emergence of modulation structure in LuFe₂O_4+x is then revealed using DSA, attesting the implication of DSA in unveiling structural distortions either locally or periodically. Inspired by the simple principle of DSA, such method can be used for any atomic-resolution images, including TEM, STM, and AFM images to exhibit the atomic displacement intuitively.