The projected electrostatic potential of a thick crystal is reconstructed at atomic-resolution from experimental scanning transmission electron microscopy data recorded using a new generation fast- readout electron camera. This practical and deterministic inversion of the equations encapsulating multiple scattering that were written down by Bethe in 1928 removes the restriction of established methods to ultrathin ($lesssim 50$ {AA}) samples. Instruments already coming on-line can overcome the remaining resolution-limiting effects in this method due to finite probe-forming aperture size, spatial incoherence and residual lens aberrations.
Atomic vibrations control all thermally activated processes in materials including diffusion, heat transport, phase transformations, and surface chemistry. Recent developments in monochromated, aberration-corrected scanning transmission electron microscopy (STEM) have enabled nanoscale probing of vibrational modes using a focused electron beam. However, to date, no experimental atomic resolution vibrational spectroscopy has been reported. Here we demonstrate atomic resolution by exploiting localized impact excitations of vibrational modes in materials. We show that the impact signal yields high spatial resolution in both covalent and ionic materials, and atomic resolution is available from both optical and acoustic vibrational modes. We achieve a spatial resolution of better than 2 {AA} which is an order of magnitude improvement compared to previous work. Our approach represents an important technical advance that can be used to provide new insights into the relationship between the thermal, elastic and kinetic properties of materials and atomic structural heterogeneities.
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 nano-scale 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 compute 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 speed-ups by calculating the atomic resolution STEM-EELS map using the L-edge transition of Fe, for of a nanoparticle 80 AA in diameter in 16 hours, a calculation that would have taken at least 80 days using a conventional multislice approach.
Structural phase transitions and soft phonon modes pose a longstanding challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO$_{3}$ is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200~K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO$_{3}$ between 150$-$300~K, and reveal the microscopic origin of its roughly $T^{-3}$ trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.
Phase imaging in electron microscopy is sensitive to the local potential including charge redistribution from bonding. We demonstrate that electron ptychography provides the necessary sensitivity to detect this subtle effect by directly imaging the charge redistribution in single layer boron nitride. Residual aberrations can be measured and corrected post-collection, and simultaneous atomic number contrast imaging provides unambiguous sub-lattice identification. Density functional theory calculations confirm the detection of charge redistribution.
Quantitative differential phase contrast imaging of materials in atomic-resolution scanning transmission electron microscopy using segmented detectors is limited by various factors, including coherent and incoherent aberrations, detector positioning and uniformity, and scan-distortion. By comparing experimental case studies of monolayer and few-layer graphene with image simulations, we explore which parameters require the most precise characterisation for reliable and quantitative interpretation of the reconstructed phases. Coherent and incoherent lens aberrations are found to have the most significant impact. For images over a large field of view, the impact of noise and non-periodic boundary conditions are appreciable, but in this case study have less of an impact than artefacts introduced by beam deflections coupling to beam scanning (imperfect tilt-shift purity).
Hamish G. Brown
,Zhen Chen
,Matthew Weyland
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(2018)
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"Structure retrieval at atomic resolution in the presence of multiple scattering of the electron probe"
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Hamish Brown
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