Linear-scaling algorithm for rapid computation of inelastic transitions in the presence of multiple electron scattering

Strong multiple scattering of the probe in scanning transmission electron microscopy (STEM) means image simulations are usually required for quantitative interpretation and analysis of elemental maps produced by electron energy-loss spectroscopy (EELS). These simulations require a full quantum-mechanical treatment of multiple scattering of the electron beam, both before and after a core-level inelastic transition. Current algorithms scale quadratically and can take up to a week to calculate on desktop machines even for simple crystal unit cells and do not scale well to the nanoscale heterogeneous systems that are often of interest to materials science researchers. We introduce an algorithm with linear scaling that typically results in an order of magnitude reduction in computation time for these calculations without introducing additional error and discuss approximations that further improve computational scaling for larger-scale objects with modest penalties in calculation error. We demonstrate these speedups by calculating the atomic resolution STEM-EELS map using the L-edge transition of Fe, for a nanoparticle 80 Å in diameter, in 16 hours, a calculation that would have taken at least 80 days using a conventional multislice approach

Patterned probes for high precision 4D-STEM bragg measurements.

Nanoscale strain mapping by four-dimensional scanning transmission electron microscopy (4D-STEM) relies on determining the precise locations of Bragg-scattered electrons in a sequence of diffraction patterns, a task which is complicated by dynamical scattering, inelastic scattering, and shot noise. These features hinder accurate automated computational detection and position measurement of the diffracted disks, limiting the precision of measurements of local deformation. Here, we investigate the use of patterned probes to improve the precision of strain mapping. We imprint a "bullseye" pattern onto the probe, by using a binary mask in the probe-forming aperture, to improve the robustness of the peak finding algorithm to intensity modulations inside the diffracted disks. We show that this imprinting leads to substantially improved strain-mapping precision at the expense of a slight decrease in spatial resolution. In experiments on an unstrained silicon reference sample, we observe an improvement in strain measurement precision from 2.7% of the reciprocal lattice vectors with standard probes to 0.3% using bullseye probes for a thin sample, and an improvement from 4.7% to 0.8% for a thick sample. We also use multislice simulations to explore how sample thickness and electron dose limit the attainable accuracy and precision for 4D-STEM strain measurements

Real time imaging of two-dimensional iron oxide spherulite nanostructure formation

The formation of complex hierarchical nanostructures has attracted a lot of attention from both the fundamental science and potential applications point of view. Spherulite structures with radial fibrillar branches have been found in various solids; however, their growth mechanisms remain poorly understood. Here, we report real time imaging of the formation of two-dimensional (2D) iron oxide spherulite nanostructures in a liquid cell using transmission electron microscopy (TEM). By tracking the growth trajectories, we show the characteristics of the reaction front and growth kinetics. Our observations reveal that the tip of a growing branch splits as the width exceeds certain sizes (5.5–8.5 nm). The radius of a spherulite nanostructure increases linearly with time at the early stage, transitioning to nonlinear growth at the later stage. Furthermore, a thin layer of solid is accumulated at the tip and nanoparticles from secondary nucleation also appear at the growing front which later develop into fibrillar branches. The spherulite nanostructure is polycrystalline with the co-existence of ferrihydrite and Fe3O4 through-out the growth. A growth model is further established, which provides rational explanations on the linear growth at the early stage and the nonlinearity at the later stage of growth. [Figure not available: see fulltext.]

Direct imaging of short-range order and its impact on deformation in Ti-6Al.

Chemical short-range order (SRO) within a nominally single-phase solid solution is known to affect the mechanical properties of alloys. While SRO has been indirectly related to deformation, direct observation of the SRO domain structure, and its effects on deformation mechanisms at the nanoscale, has remained elusive. Here, we report the direct observation of SRO in relation to deformation using energy-filtered imaging in a transmission electron microscope (TEM). The diffraction contrast is enhanced by reducing the inelastically scattered electrons, revealing subnanometer SRO-enhanced domains. The destruction of these domains by dislocation planar slip is observed after ex situ and in situ TEM mechanical testing. These results confirm the impact of SRO in Ti-Al alloys on the scale of angstroms. The direct confirmation of SRO in relationship to dislocation plasticity in metals can provide insight into how the mechanical behavior of concentrated solid solutions by the material's thermal history

Exploring the origins of perpendicular magnetic anisotropy in amorphous Tb-Co via changes in medium-range ordering

Amorphous thin films of Tb$_{17}$Co$_{83}$ (a-Tb-Co) grown by magnetron co-sputtering exhibit changes in magnetic anisotropy with varying growth and annealing temperatures. The magnetic anisotropy constant increases with increasing growth temperature, which is reduced or vanishes upon annealing at temperatures above the growth temperature. The proposed explanation for this growth-induced anisotropy in high orbital moment Tb-based transition metal alloys such as a-Tb-Co is an amorphous phase texturing with preferential in-plane and out-of-plane local bonding configurations for the rare-earth and transition metal atoms. Scanning nanodiffraction performed in a transmission electron microscope (TEM) is applied to a-Tb$_{17}$Co$_{83}$ films deposited over a range of temperatures to measure relative changes in medium-range ordering (MRO). These measurements reveal an increase in MRO with higher growth temperatures and a decrease in MRO with higher annealing temperatures. The trend in MRO indicates a relationship between the magnetic anisotropy and local atomic ordering. Tilting select films between 0$^{\circ}$ and 40$^{\circ}$ in the TEM measures variations in the local atomic structure a function of orientation within the films. The findings support claims that preferential ordering along the growth direction results from temperature-mediated adatom configurations during deposition, and that oriented MRO correlates with the larger anisotropy constants.Comment: 13 pages, 9 figure

Nanoscale mosaicity revealed in peptide microcrystals by scanning electron nanodiffraction.

Changes in lattice structure across sub-regions of protein crystals are challenging to assess when relying on whole crystal measurements. Because of this difficulty, macromolecular structure determination from protein micro and nanocrystals requires assumptions of bulk crystallinity and domain block substructure. Here we map lattice structure across micron size areas of cryogenically preserved three-dimensional peptide crystals using a nano-focused electron beam. This approach produces diffraction from as few as 1500 molecules in a crystal, is sensitive to crystal thickness and three-dimensional lattice orientation. Real-space maps reconstructed from unsupervised classification of diffraction patterns across a crystal reveal regions of crystal order/disorder and three-dimensional lattice tilts on the sub-100nm scale. The nanoscale lattice reorientation observed in the micron-sized peptide crystal lattices studied here provides a direct view of their plasticity. Knowledge of these features facilitates an improved understanding of peptide assemblies that could aid in the determination of structures from nano- and microcrystals by single or serial crystal electron diffraction

Competition between exchange and magnetostatic energies in domain pattern transfer from BaTiO₃(111) to a Ni thin film

We use spin-polarized low-energy electron microscopy to investigate domain pattern transfer in a multiferroic heterostructure consisting of a (111)-oriented BaTiO3 substrate and an epitaxial Ni film. After in situ thick-film deposition and annealing through the ferroelectric phase transition, interfacial strain transfer from ferroelastic domains in the substrate and inverse magnetostriction in the magnetic thick film introduce a uniaxial in-plane magnetic anisotropy that rotates by 60∘ between alternating stripe regions. We show that two types of magnetic domain wall can be initialized in principle. Combining experimental results with micromagnetic simulations, we show that a competition between the exchange and magnetostatic energies in these domain walls has a strong influence on the magnetic domain configuration