On the importance of fifth-order spherical aberration for a fully corrected electron microscope

Quantum Limits of Transmission Electron Microscopy

New-generation transmission electron microscopes (TEMs) are equipped with detectors that approach the shot-noise limit. Hence it is pertinent to ask: What are the quantum limits of electron scattering experiments in the TEM? For example, for a given electron dose, what is the ultimate accuracy allowed by quantum mechanics for the atomic structure of a material? We provide quantitative answers based on quantum estimation theory. We also show that, for an arbitrary set of sample parameters, the quantum limit is achievable under conditions of weak scattering, but not strong multiple scattering (this conclusion extends to scattering of other types of radiation). Implications for structure determination of radiation-sensitive materials are discussed.

Aberration correction for low voltage optimized transmission electron microscopy

Further development of low voltage electron microscopy leads to an aberration correction of the device in order to improve its spatial resolution. The integration of a corrector to a desktop transmission electron microscope with exclusively low-voltage design seems to be a challenging task. The benefits and potential of the Rose hexapole corrector implemented to such a system are critically considered in this paper. The feasibility of miniaturized corrector suitable for desktop LVEM is especially discussed, including the aspect of corrector contribution to chromatic aberration that appears to be crucial. Optimal corrector parameters and resolution limits of such a system are proposed.

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Improved spatial resolution

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Spherical aberration correction

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Permanent magnet transfer lenses

A quantitative method for measuring small residual beam tilts in high-resolution transmission electron microscopy

In a transmission electron microscope, electron illumination beam tilt, or the degree of deviation of electron beam from its optical axis, is an important parameter that has a significant impact on image contrast and image interpretation. Although a large beam tilt can easily be noticed and corrected by the standard alignment procedure, a small residual beam tilt is difficult to measure and, therefore, difficult to account for quantitatively. Here we report a quantitative method for measuring small residual beam tilts, including its theoretical schemes, numerical simulation testing and experimental verification. Being independent of specimen thickness and taking specimen drifts into account in measurement, the proposed method is supplementary to the existing "rotation center" and "coma-free" alignment procedures. It is shown that this method can achieve a rather good accuracy of 94% in measuring small residual beam tilts of about 0.1° or less.

Computation in electron microscopy

Some uses of the computer and computation in high-resolution transmission electron microscopy are reviewed. The theory of image calculation using Bloch wave and multislice methods with and without aberration correction is reviewed and some applications are discussed. The inverse problem of reconstructing the specimen structure from an experimentally measured electron microscope image is discussed. Some future directions of software development are given.

Artefacts in geometric phase analysis of compound materials

The geometric phase analysis (GPA) algorithm is known as a robust and straightforward technique that can be used to measure lattice strains in high resolution transmission electron microscope (TEM) images. It is also attractive for analysis of aberration-corrected scanning TEM (ac-STEM) images that resolve every atom column, since it uses Fourier transforms and does not require real-space peak detection and assignment to appropriate sublattices. Here it is demonstrated that, in ac-STEM images of compound materials with compositionally distinct atom columns, an additional geometric phase is present in the Fourier transform. If the structure changes from one area to another in the image (e.g. across an interface), the change in this additional phase will appear as a strain in conventional GPA, even if there is no lattice strain. Strategies to avoid this pitfall are outlined.

Controlled radiation damage and edge structures in boron nitride membranes

We show that hexagonal boron nitride membranes synthesized by chemical exfoliation are more resistant to electron beam irradiation at 80 kV than is graphene, consistent with quantum chemical calculations describing the radiation damage processes. Monolayer hexagonal boron nitride does not form vacancy defects or amorphize during extended electron beam irradiation. Zigzag edge structures are predominant in thin membranes for both a freestanding boron nitride monolayer and for a supported multilayer step edge. We have also determined that the elemental termination species in the zigzag edges is predominantly N.

Atomic structure imaging beyond conventional resolution limits in the transmission electron microscope

Transmission electron microscopy is an extremely powerful technique for direct characterization of local structure at the atomic scale. However, the resolution of this technique is fundamentally limited by the partial coherence of the electron beam. In this Letter we demonstrate a method that extends the ultimate resolution of the latest generation of aberration corrected transmission electron microscopes by 41% relative to that achievable using conventional axial imaging. Experimental results verify that a real space resolution of 78 pm has been achieved at 200 kV.

Particle size determination using TEM: a discussion of image acquisition and analysis for the novice microscopist

As nanoparticle synthesis capabilities advance, there is an increasing need for reliable nanoparticle size distribution analysis. Transmission electron microscopy (TEM) can be used to directly image nanoparticles at scales approaching a single atom. However, the advantage gained by being able to "see" these nanoparticles comes with several tradeoffs that must be addressed and balanced. For effective nanoparticle characterization, the proper selection of imaging type (bright vs dark field), magnification, and analysis method (manual vs automated) is critical. These decisions control the measurement resolution, the contrast between the particle and background, the number of particles in each image, the subsequent analysis efficiency, and the proper determination of the particle-background boundary and affect the significance of electron beam damage to the sample. In this work, the relationship between the critical decisions required for TEM analysis of small nanoparticles and the statistical effects of these factors on the resulting size distribution is presented.

Low-dose aberration corrected cryo-electron microscopy of organic specimens

Spherical aberration (C(s)) correction in the transmission electron microscope has enabled sub-angstrom resolution imaging of inorganic materials. To achieve similar resolution for radiation-sensitive organic materials requires the microscope to be operated under hybrid conditions: low electron dose illumination of the specimen at liquid nitrogen temperature and low defocus values. Initial images from standard inorganic and organic test specimens have indicated that under these conditions C(s)-correction can provide a significant improvement in resolution (to less than 0.16nm) for direct imaging of organic samples.

Contrast transfer and resolution limits for sub-angstrom high-resolution transmission electron microscopy

The optimum imaging of an object structure at the sub-angstrom length scale requires precise adjustment of the lens aberrations of a high-resolution instrument up to the fifth order. A least-squares optimization of defocus aberration C1, third-order spherical aberration C3, and fifth-order spherical aberration C5 yields two sets of aberration coefficients for strong phase contrast up to the information limit: one for variable C1 and C3, at fixed C5, another for variable C1, C3, and C5. An additional correction to the defocus aberration, dependent on object thickness, is described, which becomes important for the use of image simulation programs in predicting optimum high-resolution contrast from thin objects at the sub-angstrom scale. For instruments with a sub-angstrom information limit the ultimate structure resolution, the power to resolve adjacent atom columns in a crystalline object, depends on both the instrumental pointspread and an object pointspread due to finite width of the atomic column potentials. A simulation study on a simple double-column model yields a range for structure resolutions, dependent on the atomic scattering power, from 0.070 nm down to 0.059 nm, for a hypothetical 300-kV instrument with an information limit of 0.050 nm.