As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 μm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.

The atomic reconstruction of a misfit dislocation (MD) core causes change in the strain distribution around the core. Several MD cores at the AlSb/GaAs (001) cubic zincblende interface, including a symmetrical glide set Lomer dislocation (LD), a left-displaced glide set LD, a glide set LD with an atomic step, a symmetrical shuffle set LD, and a 60° dislocation pair, were studied using simulated projected potential and aberration-corrected transmission electron microscope images. Image deconvolution was also used to restore structure images from nonoptimum-defocus images. The corresponding biaxial strain maps, εxx (in-plane) and εyy (out-of-plane), were obtained by geometric phase analysis using the GaAs substrate as the reference lattice. The results show that atomic structure characteristics of MD cores can be revealed by the strain maps. The strain maps should be measured from optimum-defocus images or restored structure images. Furthermore, the εxx strain map has been found more accurate than the εyy strain map for MD cores, and the specimen thickness should be below the critical thickness due to the influence of dynamical scattering.

New methods for defect analysis can lead to improved interpretation of experimental data and thus better understanding of material properties. Although transmission electron microscopy (TEM) has been used to study defects for many decades, interpretive ambiguities can arise for cases that seem simple or even trivial. Using geometric phase analysis (GPA), an image processing procedure, we show that an apparent simple line defect in pyrite has an entirely different character. It appears to be a b = ½[100] edge dislocation as viewed in a [001] high-resolution TEM (HRTEM) image, but the measured ux and uy displacements are asymmetric, which is inconsistent with a simple line dislocation. Instead, the defect is best understood as a terminating {101} marcasite slab in pyrite. The simulated HRTEM image based on this model reproduces the defect contrast and illustrates the power of GPA analysis for (1) avoiding potential pitfalls of misinterpreting apparently simple defects in HRTEM images, (2) detecting differences in elastic properties at the atomic scale, and (3) providing data for the positions of atom columns, thereby facilitating the construction of structure models for complex defects.

In this article a method for determining errors of the strain values when applying strain mapping techniques has been devised. This methodology starts with the generation of a thickness/defocus series of simulated high-resolution transmission electron microscopy images of InAsxP1−x/InP heterostructures and the application of geometric phase. To obtain optimal defocusing conditions, a comparison of different defocus values is carried out by the calculation of the strain profile standard deviations among different specimen thicknesses. Finally, based on the analogy of real state strain to a step response, a characterization of strain mapping error near an interface is proposed.