Convergent beam electron holography for analysis of van der Waals heterostructures

The van der Waals heterostructures, which explore the synergetic properties of 2D materials when assembled into 3D stacks, have already brought to life a number of exciting phenomena and electronic devices. Still, the interaction between the layers in such assembly, possible surface reconstruction, and intrinsic and extrinsic defects are very difficult to characterize by any method, because of the single-atomic nature of the crystals involved. Here we present a convergent beam electron holographic technique which allows imaging of the stacking order in such heterostructures. Based on the interference of electron waves scattered on different crystals in the stack, this approach allows one to reconstruct the relative rotation, stretching, and out-of-plane corrugation of the layers with atomic precision. Being holographic in nature, our approach allows extraction of quantitative information about the 3D structure of the typical defects from a single image covering thousands of square nanometers. Furthermore, qualitative information about the defects in the stack can be extracted from the convergent diffraction patterns even without reconstruction, simply by comparing the patterns in different diffraction spots. We expect that convergent beam electron holography will be widely used to study the properties of van der Waals heterostructures.

Nanoscale symmetry fluctuations in ferroelectric barium titanate, BaTiO3

Crystal charge density is a ground-state electronic property. In ferroelectrics, charge is strongly influenced by lattice and vice versa, leading to a range of interesting temperature-dependent physical properties. However, experimental determination of charge in ferroelectrics is challenging because of the formation of ferroelectric domains. Demonstrated here is the scanning convergent-beam electron diffraction (SCBED) technique that can be simultaneously used for imaging ferroelectric domains and identifying crystal symmetry and its fluctuations. Results from SCBED confirm the acentric tetragonal, orthorhombic and rhombohedral symmetry for the ferroelectric phases of BaTiO₃. However, the symmetry is not homogeneous; regions of a few tens of nanometres retaining almost perfect symmetry are interspersed in regions of lower symmetry. While the observed highest symmetry is consistent with the displacive model of ferroelectric phase transitions in BaTiO₃, the observed nanoscale symmetry fluctuations are consistent with the predictions of the order-disorder phase-transition mechanism.

Mapping of Strain Fields in GaAs/GaAsP Core-Shell Nanowires with Nanometer Resolution

We report the nanoscale quantification of strain in GaAs/GaAsP core-shell nanowires. By tracking the shifting of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction patterns, we observe unique variations in HOLZ line separation along different facets of the core-shell structure, demonstrating the nonuniform strain fields created by the heterointerface. Furthermore, through the use of continuum mechanical modeling and Bloch wave analysis we calculate expected HOLZ line shift behavior, which are directly matched to experimental results. This comparison demonstrates both the power of electron microscopy as a platform for nanoscale strain characterization and the reliability of continuum models to accurately calculate complex strain fields in nanoscale systems.

Observing (non)linear lattice dynamics in graphite by ultrafast Kikuchi diffraction

In materials, the nature of the strain-stress relationship, which is fundamental to their properties, is determined by both the linear and nonlinear elastic responses. Whereas the linear response can be measured by various techniques, the nonlinear behavior is nontrivial to probe and to reveal its nature. Here, we report the methodology of time-resolved Kikuchi diffraction for mapping the (non)linear elastic response of nanoscale graphite following an ultrafast, impulsive strain excitation. It is found that the longitudinal wave propagating along the c-axis exhibits echoes with a frequency of 9.1 GHz, which indicates the reflections of strain between the two surfaces of the material with a speed of ∼4 km/s. Because Kikuchi diffraction enables the probing of strain in the transverse direction, we also observed a higher-frequency mode at 75.5 GHz, which has a relatively long lifetime, on the order of milliseconds. The fluence dependence and the polarization properties of this nonlinear mode are entirely different from those of the linear, longitudinal mode, and here we suggest a localized breather motion in the a-b plane as the origin of the nonlinear shear dynamics. The approach presented in this contribution has the potential for a wide range of applications because most crystalline materials exhibit Kikuchi diffraction.

Direct atomic structure determination by the inspection of structural phase

A century has passed since Bragg solved the first atomic structure using diffraction. As with this first structure, all atomic structures to date have been deduced from the measurement of many diffracted intensities using iterative and statistical methods. We show that centrosymmetric atomic structures can be determined without the need to measure or even record a diffracted intensity. Instead, atomic structures can be determined directly and quickly from the observation of crystallographic phases in electron diffraction patterns. Furthermore, only a few phases are required to achieve high resolution. This represents a paradigm shift in structure determination methods, which we demonstrate with the moderately complex α-Al2O3. We show that the observation of just nine phases enables the location of all atoms with a resolution of better than 0.1 Å. This level of certainty previously required the measurement of thousands of diffracted intensities.

Geometry-induced dislocations in coaxial heterostructural nanotubes

Highly localized dislocations in GaN/ZnO hetero-nanostructures are generated from the residual strain field by lattice mismatches at two interfaces: between the substrate and hetero-nanostructures, and between the ZnO core and GaN shell. The local strain field is measured using tranmission electron microscopy, and the relationship between the nanostructure morphology and the highly localized dislocations is analyzed by a finite element method.