Focal Series Research Articles

Atomically resolved imaging of highly ordered alternating fluorinated graphene.

One of the most desirable goals of graphene research is to produce ordered two-dimensional (2D) chemical derivatives of suitable quality for monolayer device fabrication. Here we reveal, by focal series exit wave reconstruction (EWR), that C2F chair is a stable graphene derivative and demonstrates pristine long-range order limited only by the size of a functionalized domain. Focal series of images of graphene and C2F chair formed by reaction with XeF2 were obtained at 80 kV in an aberration-corrected transmission electron microscope. EWR images reveal that single carbon atoms and carbon-fluorine pairs in C2F chair alternate strictly over domain sizes of at least 150 nm(2) with electron diffraction indicating ordered domains ≥ 0.16 μm(2). Our results also indicate that, within an ordered domain, functionalization occurs on one side only as theory predicts. In addition, we show that electron diffraction provides a quick and easy method for distinguishing between graphene, C2F chair and fully fluorinated stoichiometric CF 2D phases.

Atomic-scale evolution of a growing core-shell nanoparticle.

Understanding the atomic-scale growth at solid/solution interfaces is an emerging frontier in molecular and materials chemistry. This is particularly challenging when studying chemistry occurring on the surfaces of nanoparticles in solution. Here, we provide atomic-scale resolution of growth, in a statistical approach, at the surfaces of inorganic nanoparticles by state-of-the-art aberration-corrected transmission electron microscopy (TEM) and focal series reconstruction. Using well-known CdSe nanoparticles, we unfold new information that, for the first time, allows following growth directly, and the subsequent formation of CdS shells. We correlate synthetic procedures with resulting atomic structure by revealing the distribution of lattice disorder (such as stacking faults) within the CdSe core particles. With additional sequential synthetic steps, an ongoing transformation of the entire structure occurs, such that annealing takes place and stacking faults are eliminated from the core. The general strategy introduced here can now be used to provide equally revealing atomic-scale information concerning the structural evolution of inorganic nanostructures.

TFS: Combined Tilt- and Focal Series Scanning Transmission Electron Microscopy

The primary method currently used for obtaining insight into the three-dimensional (3D) structure of unique samples from biology and materials science at the nanometer scale is tilt-series transmission electron microscopy (TEM) [1]. A 3D volume is reconstructed from images recorded at many projections obtained by mechanically tilting the sample stage. The tilt range strongly influences the resolution and characteristics of the 3D reconstructions. Therefore, one would ideally acquire tilted images covering the entire angular range of ±90°. However, in practice the maximum tilt range is usually only about ±60 -78° due to mechanical limitations of specimen holders and because the effective thickness of the specimen as seen by the electron beam increases as the section is tilted. The tomographic reconstruction then suffers from missing information and a limited resolution on account of this so-called “missing wedge”. The reconstruction of conventional tilt-series tomography data is particularly difficult because its data acquisition involves a large amount of mechanical movements of the stage. The quality of the tomogram is mostly determined by the precision of the alignment of the individual images. The alternative of recording focal-series scanning TEM (STEM) data avoids the problem caused by the mechanical movements but it lacks axial resolution [2]. We have introduced a new recording scheme for 3D STEM that significantly reduces the aforementioned two limitations of tilt series tomography. In the combined tilt- and focal series (TFS) method, the specimen is rotated in relatively large tilt increments over the possible tilt range, and for every tilt direction, a through-focal series is recorded (Fig. 1). The reconstruction method differs from existing methods such as sequential algebraic reconstruction technique (SART). Both the tilt-series and focal-series data are reconstructed into a 3D tomogram in the same software algorithm. The conical shape of the STEM probe is taken into account via forward- and backward projection operators. The TFS method was demonstrated to exhibit reduced “missing wedge” artifacts and a higher axial resolution than obtainable using STEM tilt series [3]. Fig. 2 shows that the missing wedge is still present in the TFS but in the central vertical region, low spatial frequency signal components are now present (arrow). Moreover, the streaks corresponding to the tilt directions are less pronounced in the TFS data. Amongst the most promising applications for STEM tomography with TFS are specimens that require a high precision in the representation of the 3D shapes, whereby TFS reconstruction results in a superior shape reconstruction. The combined tilt- and focal series method could potentially present a better method for atomic 3D resolution while it tolerates a much smaller number of tilt angles than tomography. We expect that a further advantage of TFS STEM can be found for the imaging of micrometers-thick samples. The largest problem when imaging thick samples occurs at the high tilt

Exit wave reconstruction of radiation-sensitive materials from low-dose data

We report exit wave reconstruction using a focal series of low-dose images for ZSM-5, a zeolite which has a wide range of industrial applications. The exit wave phase was successfully reconstructed showing the structure of ZSM-5 at a near-atomic resolution even though the dose in the individual images in the focal series was as low as 26 electrons/Å2. This implementation shows the method's potential for application to other radiation-sensitive materials.

Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series

In this study, a combined tilt- and focal series is proposed as a new recording scheme for high-angle annular dark-field scanning transmission electron microscopy (STEM) tomography. Three-dimensional (3D) data were acquired by mechanically tilting the specimen, and recording a through-focal series at each tilt direction. The sample was a whole-mount macrophage cell with embedded gold nanoparticles. The tilt-focal algebraic reconstruction technique (TF-ART) is introduced as a new algorithm to reconstruct tomograms from such combined tilt- and focal series. The feasibility of TF-ART was demonstrated by 3D reconstruction of the experimental 3D data. The results were compared with a conventional STEM tilt series of a similar sample. The combined tilt- and focal series led to smaller "missing wedge" artifacts, and a higher axial resolution than obtained for the STEM tilt series, thus improving on one of the main issues of tilt series-based electron tomography.

Testing the accuracy of the two-dimensional object model in HAADF STEM

In high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) the two-dimensional (2D) object-function approximation and image convolution model is often used to describe the recorded image data from on-axis crystalline samples. In this model the sample, represented by an object function with sharp peaks at the atomic column positions, is convolved with the 2D point spread function (PSF) of the focussed STEM illumination. In this work the validity of the assumption that the object can be considered as 2D is evaluated experimentally through the use of HAADF-STEM focal-series from MgO smoke cubes. The intensity of laterally resolved image-information is evaluated using Fourier transforms and is tracked with respect to defocus. The experimental results are compared with the expected depth resolution capabilities of simulated STEM probes to yield the normalised or ‘apparent thickness’ of the samples. The 2D object-function and image convolution models are found to hold for sample thicknesses of up to 250nm. As the 2D object model holds true for each individual frame in a recorded focal series, we can hence express the focal-series as a whole as the convolution of a 2D object function with a 3D probe function with implications for both the diagnosis of remnant aberrations and also image reconstruction.

Towards full-resolution inline electron holography

With the availability of fast computers, inline electron holography, a technique for reconstructing both amplitude and phase of the electron wave function as scattered by the sample from a set of differently aberrated transmission electron microscopy images, is becoming increasingly quantitative. While focal series reconstruction from transmission electron microscopy images has already been practiced for at least 3 decades, existing approaches can only recover a relatively small band of spatial frequencies. Here I present a reconstruction scheme which is capable of reconstructing the electron wave function for a very large range of spatial frequencies, demonstrating its performance using simulated as well as experimental data.

Recording low and high spatial frequencies in exit wave reconstructions

Aberration corrected Transmission Electron Microscope (TEM) images can currently resolve information at significantly better than 0.1 nm. Aberration corrected imaging conditions seek to optimize the transfer of high-resolution information but in doing so they prevent the transfer of low spatial frequency information. To recover low spatial frequency information, aberration corrected images must be acquired at a large defocus which compromises high spatial frequency information transfer. In this paper we present two a posteriori solutions to this problem in which the information bandwidth in an exit wave reconstruction is increased. In the first we reconstruct the electron exit wavefunction from two focal series datasets, with different, uniform focal steps, experimentally demonstrating that the width of the transfer interval can be extended from 0.2 nm⁻¹ (∼5 nm) to better than 10 nm⁻¹ (0.1 nm). In the second we outline the use of a focal series recorded with a non-uniform focal step to recover a wider range of spatial frequencies without the need for a large number of images. Using simulated data we show that using this non-uniform focal step the spatial frequency interval for a five image data set may be increased to between 0.25 nm⁻¹ (4 nm) and 8.3 nm⁻¹ (0.12 nm) compared to between 0.74 nm⁻¹ (1.4 nm) and 8.3 nm⁻¹ (0.12 nm) for the standard focal series geometry.

Observation of the atomic structure of ß′-SiAlON using three generations of high resolution electron microscopes

The structure of a ß′-SiAlON (Si5.6Al0.4O0.4N7.6) has been observed using three generations of unique high resolution microscopes spanning over three decades of development in instrumentation – the Atomic Resolution Microscope (ARM), the One Angstrom Microscope (OAM) and the Transmission Electron Aberration-corrected Microscope (TEAM). The information limits of these microscopes are 0.16, 0.08 and 0.05 nm respectively. Observations along ⟨0 0 0 1⟩ at Scherzer defocus for each microscope demonstrate a drastic increase in structural information. Images taken on TEAM show clearly resolved atomic columns whereas the ARM images were only indirectly related to the structure. Nevertheless, the loss of the six-fold symmetry associated with the O/N and Al/Si substitutions was already visible on images taken on the ARM, and an associated ∼25 pm displacement of the O substituting for N in some of the 2c Wyckoff positions of the SiN unit cell was measured on exit wave reconstructions obtained from through focal series on the OAM. This paper illustrates how progress in instrumentation impacts our analysis and understanding of materials.

The Influence of the Sample Thickness on the Lateral and Axial Resolution of Aberration-Corrected Scanning Transmission Electron Microscopy

The lateral and axial resolution of three-dimensional (3D) focal series aberration-corrected scanning transmission electron microscopy was studied for samples of different thicknesses. The samples consisted of gold nanoparticles placed on the top and at the bottom of silicon nitride membranes of thickness between 50 and 500 nm. Atomic resolution was obtained for nanoparticles on top of 50-, 100-, and 200-nm-thick membranes with respect to the electron beam traveling downward. Atomic resolution was also achieved for nanoparticles placed below 50-, 100-, and 200-nm-thick membranes but with a lower contrast at the larger thicknesses. Beam broadening led to a reduced resolution for a 500-nm-thick membrane. The influence of the beam broadening on the axial resolution was also studied using Monte Carlo simulations with a 3D sample geometry.

External granular cell layer bobbling: a distinct histomorphological feature of the developing human cerebellum

The external granular layer (EGL) of the developing human cerebellum is detectable until an age of ~ 1 year. It has been described as a thin, evenly calibrated layer of germinal cells. We have repeatedly observed a distinct discontinuous bobbled configuration of the EGL (external granular layer bobbling = EGLB) in human infantile autopsy brains. AIM, MATERIALS AND METHODS: We investigated 106 human fetal and infantile postmortem brains (range of gestational week at birth: 14 - term; range of postpartal age: 0 - 500 days) for presence of EGLB and correlated it with gestational/postpartal age, gender, developmental stage of cerebellar cortex, medical history and neuropathological findings. EGLB was detectable in 38/106 (35.8%) cases. EGLB presents as focal series of uniform knob-like protrusions of the EGL. In the notches between individual knobs, capillaries penetrate from the primitive leptomeningeal vascular plexus into the molecular layer. We found EGLB predominantly in depths of fissures of cerebellar hemispheres, vermis and/or tonsils. Presence of EGLB was statistically significantly more common in liveborn cases who died after gestational week 25 and cases with higher maturity grade of the cerebellar cortex, respectively. There was no gender difference. EGLB was not associated with medical history or neuropathological findings. EGLB is a distinct histomorphological feature of the developing cerebellum, which is predominantly found in infants. Our data indicate that EGLB is a physiological phenomenon occuring during cerebellar development at a certain gestational age, although we cannot exclude that it represents an artifact related to tissue fixation. In any case, recognition of this recurring feature is relevant for the practicing neuropathologist and should not be interpreted as a cerebellar migration disorder.

Atomic Resolution Phase Contrast Imaging and In-Line Holography Using Variable Voltage and Dose Rate

The TEAM 0.5 electron microscope is employed to demonstrate atomic resolution phase contrast imaging and focal series reconstruction with acceleration voltages between 20 and 300 kV and a variable dose rate. A monochromator with an energy spread of ≤0.1 eV is used for dose variation by a factor of 1,000 and to provide a beam-limiting aperture. The sub-Ångstrøm performance of the instrument remains uncompromised. Using samples obtained from silicon wafers by chemical etching, the [200] atom dumbbell distance of 1.36 Å can be resolved in single images and reconstructed exit wave functions at 300, 80, and 50 kV. At 20 kV, atomic resolution <2 Å is readily available but limited by residual lens aberrations at large scattering angles. Exit wave functions reconstructed from images recorded under low dose rate conditions show sharper atom peaks as compared to high dose rate. The observed dose rate dependence of the signal is explained by a reduction of beam-induced atom displacements. If a combined sample and instrument instability is considered, the experimental image contrast can be matched quantitatively to simulations. The described development allows for atomic resolution transmission electron microscopy of interfaces between soft and hard materials over a wide range of voltages and electron doses.

Strain mapping of LED devices by dark-field inline electron holography: Comparison between deterministic and iterative phase retrieval approaches

Dark-field inline electron holography has recently been established as a convenient method to map strain in semiconductor devices, combining high precision, low noise, sub-nm spatial resolution and fields-of-view larger than 1 μm. Here we compare two approaches to reconstruct the geometric phase from a transmission electron microscopy dark-field focal series and their effects on the strain measurement: the transport-of-intensity-equation (TIE) and a flux-preserving iterative approach. For this task, we used a GaN-based light emitting diode with a highly complex heterostructure as a model system. While the TIE relies on 3 images only but requires the optimization of two free parameters (defocus step and low-limit cut-off frequency), the iterative reconstruction algorithm involves no adjustable parameters and uses images recorded at 9 different planes of focus with quadratically increasing defocus values. Optimum parameters for the TIE-reconstruction could be identified. However, the iterative phase retrieval approach yields the strain values that agree best with the expected strain levels and provides also higher spatial resolution.

STEM Image Post-processing for Instability and Aberration Correction for Transfer Function Extension

Scanning transmission electron microscopy (STEM) images can be limited by either aberrations or, because of the technique's serial acquisition, by the effects of environmental instabilities. MatLab image-processing code was written which performs a two stage process to restore degraded high-resolution high-angle annular dark-field (HAADF) STEM images. Firstly, individual images were analysed to identify and correct for high-frequency scan noise; image resolution and signal-noise ratio (SNR) are used as performance metrics and were improved by up to 11.8% and 49% respectively. Secondly, a focal series was used to identify variations in information transfer as a function of defocus (aberrations) whereafter a single image was reconstructed yielding an increase in resolution and SNR of 9.88% and 205% respectively.

Exit wave reconstruction from focal series of HRTEM images, single crystal XRD and total energy studies on SbxWO3+y(x∼ 0.11)

A new tungsten bronze in the Sb—W—O system has been prepared in a solid state reaction from Sb 2 O 3 , WO 3 and W metal powder. The average structure was determined by single crystal X-ray diffraction. Sb x WO 3+ y ( x ∼ 0.11) crystallizes in the orthorhombic space group Pm 2 1 n (no. 31), a = 27.8135(9) Å, b = 7.3659(2) Å and c = 3.8672(1) Å. The structure belongs to the ( n )-ITB class of intergrowth tungsten bronzes. It contains slabs of hexagonal channels formed by six WO 6 octahedra. These slabs are separated by three layers of WO 6 octahedra that are arranged in a WO 3 -type fashion. The WO 6 octahedra share all vertices to build up a three-dimensional framework. The hexagonal channels are filled with Sb atoms to ∼80% and additional O atoms. The atoms are shifted out of the center of the channels. Exit-wave reconstruction of focal series of high resolution-transmission-electron-microscope (HRTEM) images combined with statistical paramäeter estimation techniques allowed to study local ordering in the channels. Sb atoms in neighbouring channels tend to be displaced in the same direction, which is in agreement with total energy calculations on ordered structure models, but the ratio of the occupation of the two possible Sb sites varies from channel to channel. The structure of Sb x WO 3+ y exhibits pronounced local modulations.

Using a monochromator to improve the resolution in TEM to below 0.5Å. Part II: Application to focal series reconstruction

We apply monochromated illumination to improve the information transfer in focal series reconstruction to 0.5 Å at 300 kV. Contrary to single images, which can be taken arbitrarily close to Gaussian focus in a C(S)-corrected microscope, images in a focal series are taken at a certain defocus. This defocus poses limits on the spatial coherence of the illumination, and through this, limits on the brightness of the monochromated illumination. We derive an estimate for the minimum spatial coherence and the minimal brightness needed for a certain resolution at a certain defocus and apply this estimate to our focal series experiments. We find that the 0.5 Å information transfer would have been difficult and probably impossible to obtain without the exceptionally high brightness of the monochromated illumination.

Morphology, structure, and chemistry of nanoclusters in a mechanically alloyed nanostructured ferritic steel

Nanostructured ferritic steels have excellent elevated temperature strengths, creep resistances, and radiation tolerances due to the presence of a high density of Ti–Y–O-enriched nanoclusters. The compositions, morphologies, and structures of the smallest of these nanoclusters with maximum dimensions of ~2–4 nm were investigated in alloy 14YWT by high-resolution scanning transmission electron microscopy and atom probe tomography. Nanoclusters are found to be coherent with truncated rhombic dodecahedron morphologies defined by the {100} and {110} planes in the Fe matrix. Particles have compositions rich in Ti, O, Y, and Cr that are inconsistent with known oxide structures. The smallest nanoclusters appear to lack an identifiable crystal structure. Both nano-diffraction and focal series imaging through the sample thickness suggest that they are amorphous.

Study of coherence strain of GP II zones in an aged aluminum composite

Strain mapping using the geometric phase analysis (GPA) technique was applied to Al–GP II (Guinier–Preston) nanoscale precipitates, using both high resolution transmission electron microscopy (HRTEM) micrographs as well as the exit wave function (EWF) obtained by focal series reconstruction. The experimental strain results were compared with strain maps obtained from an atomic model which consisted of an Al supercell containing a GP II precipitate. It was built as a reference from literature data. The experimental results demonstrate a complex strain distribution and larger fluctuations than the reference strain maps. These differences were found to be partly a consequence of image artifacts produced by the technique as well as complex microstructural events which were present at the development stage studied.

Optimized Deconvolution for Maximum Axial Resolution in Three-Dimensional Aberration-Corrected Scanning Transmission Electron Microscopy

Three-dimensional (3D) datasets were recorded of gold nanoparticles placed on both sides of silicon nitride membranes using focal series aberration-corrected scanning transmission electron microscopy (STEM). Deconvolution of the 3D datasets was applied to obtain the highest possible axial resolution. The deconvolution involved two different point spread functions, each calculated iteratively via blind deconvolution. Supporting membranes of different thicknesses were tested to study the effect of beam broadening on the deconvolution. It was found that several iterations of deconvolution was efficient in reducing the imaging noise. With an increasing number of iterations, the axial resolution was increased, and most of the structural information was preserved. Additional iterations improved the axial resolution by maximal a factor of 4 to 6, depending on the particular dataset, and up to 8 nm maximal, but also led to a reduction of the lateral size of the nanoparticles in the image. Thus, the deconvolution procedure optimized for the highest axial resolution is best suited for applications where one is interested in the 3D locations of nanoparticles only.

Toward electron exit wave tomography of amorphous materials at atomic resolution

We suggest to use electron exit wave phase for tomographic reconstruction of structure of Au-doped amorphous Si with atomic resolution. In the present theoretical investigation into the approach it is found that the number of projections and the accuracy of defocus in the focal series restoration are the main factors that contribute to the final resolution. Although resolution is ultimately limited by these factors, phase shifts in the exit wave are sufficient to identify the position of Au atoms in an amorphous Si needle model, even when only 19 projections with defocus error of 4nm are used. Electron beam damage will probably further limit the resolution of such tomographic reconstructions, however beam damage can be mitigated using lower accelerating voltages.