Focal Series Reconstruction Research Articles

Synergistic use of gradient flipping and phase prediction for inline electron holography

Inline holography in the transmission electron microscope is a versatile technique which provides real-space phase information that can be used for the correction of imaging aberrations, as well as for measuring electric and magnetic fields and strain distributions. It is able to recover high-spatial-frequency contributions of the phase effectively but suffers from the weak transfer of low-spatial-frequency information, as well as from incoherent scattering. Here, we combine gradient flipping and phase prediction in an iterative flux-preserving focal series reconstruction algorithm with incoherent background subtraction that gives extensive access to the missing low spatial frequencies. A procedure for optimizing the reconstruction parameters is presented, and results from Fe-filled C nanospheres, and MgO cubes are compared with phase images obtained using off-axis holography.

Real-Space Crystal Structure Analysis by Low-Dose Focal-Series TEM Imaging of Organic Materials with Near-Atomic Resolution.

Structural analysis of beam-sensitive materials by transmission electron microscopy (TEM) represents a significant challenge, as high-resolution TEM (HRTEM) requires high electron doses that limit its applicability to stable inorganic materials. Beam-sensitive materials, e.g., organic crystals, must be imaged under low dose conditions, leading to problematic contrast interpretation and loss of fine structural details. Here, HRTEM imaging of organic crystalline materials with near-atomic resolution of up to 1.6 Å is described, which enables real-space studies of crystal structures, as well as observation of co-existing polymorphs, crystal defects, and atoms. This is made possible by a low-dose focal-series reconstruction methodology, which provides HRTEM images where contrast reflects true object structure and can be performed on contemporary cryo-EM instruments available to many research institutions. Copper phthalocyanine (CuPc), a perchlorinated analogue of CuPc, and indigo crystalline films are imaged. In the case of indigo crystals, co-existing polymorphs and individual atoms (carbonyl oxygen) can be observed. In the case of CuPc, several polymorphs are observed, including a new one, for which the crystal structure is found based on direct in-focus imaging, accomplishing real-space crystal structure elucidation. Such direct analysis can be transformative for structure studies of organic materials.

Holographic focal series: differences between inline and off-axis electron holography at atomic resolution

Electron holography methods allow phase information to be recovered from electron waves at atomic resolution. Focal-series reconstruction, an inline method, and off-axis holography are currently the most commonly employed techniques for this endeavor. By recording and reconstructing data from a holographic focal series of an atomically resolved GaAs crystal, we are able to reconstruct wave functions by means of both methods from the same measurement. Significant differences between these wave functions are found for low frequencies and in thicker specimen parts. Furthermore, in a rigorous treatment, we discuss how the recovered wave functions differ because of fundamental differences in the quantum mechanical measurement.

Revealing Growth Schemes of Nanoparticles in Atomic Resolution: Mapping Stacking Fault Formation and Distribution

Controlling the growth process of inorganic nanoparticles, especially the kinetically driven ones, is crucial for designing tailor-made nanoparticles for various applications. Specifically, controlling the formation of stacking faults in semiconductor quantum dots is necessary, since stacking faults were associated with inferior optical performance. Ensemble techniques, such as XRD powder diffraction and optical absorption, can be insensitive to the formation of stacking faults and in certain cases might produce misleading information. Using as a model the thoroughly studied CdSe system, we exploited the well-known unidirectional growth of the Wurtzite phase in order to follow the structural evolution of two different batches of CdSe nanoparticles. We were able to get insight on the crystal growth stages, step by step, employing high resolution electron microscopy and focal series reconstruction. The different kinetics of the two variants were monitored using a statistical approach. The same approach can be used to provide atomic-scale information for any system exhibiting unidirectional growth.

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.

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.

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.

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.

Using a monochromator to improve the resolution in TEM to below 0.5Å. Part I: Creating highly coherent monochromated illumination

Chromatic aberration limits the resolution in spherical-aberration corrected Transmission Electron Microscopy to approximately 0.7Å at 300 kV. The energy spread in the beam is the main contribution to the chromatic aberration. This spread can be reduced with a monochromator. Another limitation to the resolution in TEM can be the finite brightness of the source and the consequent partial spatial coherence of the illumination. This limitation becomes important when spherical aberration and/or defocus are present such as in uncorrected TEM or in focal-series reconstruction in TEM. We used a monochromator optimized for minimum brightness loss and a prototype 'high-brightness' gun, and obtained brightness after monochromation comparable to that of the standard Schottky FEG before monochromation. The images were acquired on the prototype TEAM 0.5 microscope, which was developed on a Titan platform by increasing its electrical and mechanical stability.

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.

Imaging from atomic structure to electronic structure

This paper discusses the possibility of retrieving the electron distribution (with highlighted valence electron distribution information) of materials from recorded HREM images. This process can be achieved by solving two inverse problems: reconstruction of the exit wave and reconstruction of the electron distribution from exit waves. The first inverse problem can be solved using a focal series reconstruction method. We show that the second inverse problem can be solved by combining a series of exit waves recorded at different thickness conditions. This process is designed based on an improved understanding of the dynamical scattering process. It also explains the fundamental difficulty of obtaining the valence electron distribution information and the basis of our solution.

Experimental evidence and structural modeling of nonstoichiometric (0 1 0) surfaces coexisting in hydroxyapatite nano-crystals

High-resolution transmission electron microscopy (HRTEM) and ab initio quantum-mechanical calculations of electronic structure were combined to investigate the structure of the hydroxyapatite (HA) (010) surface, which plays an important role in HA interactions with biological media. HA was synthesized by in vitro precipitation at 37°C. HRTEM images revealed thin elongated rod nanoparticles with preferential growth along the [001] direction and terminations parallel to the (010) plane. The focal series reconstruction (FSR) technique was applied to develop an atomic-scale structural model of the high-resolution images. The HRTEM simulations identified the coexistence of two structurally distinct terminations for (010) surfaces: a rather flat Ca(II)-terminated surface and a zig-zag structure with open OH channels. Density functional theory (DFT) was applied in a periodic slab plane-wave pseudopotential approach to refine details of atomic coordination and bond lengths of Ca(I) and Ca(II) sites in hydrated HA (010) surfaces, starting from the HRTEM model.

Wave-front phase retrieval in transmission electron microscopy via ptychography

There are many different strategies that allow the solving of the well-known phase problem corresponding to the loss of phase information during a physical measurement. In microscopy, and, in particular, in transmission electron microscopy, most of these strategies focus on the retrieval of high-resolution information with the importance of lower resolution data often overlooked. Ptychography offers a means to investigate such data. Ptychography is a robust diffractive imaging technique with fast convergence for phase retrieval but, until now, has not been applied at the nanoscale. In this paper, we use the ptychographical iterative engine to retrieve the phase change at the exit plane of metallic nanoparticles using a conventional transmission electron microscope. Ptychographical reconstructions yielded images with a phase resolution of $\ensuremath{\pi}/10$ and a spatial resolution of 1 nm. These results stand as a first step toward aberration-free lensless imaging. The technique lends itself to be an alternative to off-axis electron holography or focal series reconstruction.

Off-axis and inline electron holography: A quantitative comparison

Capable of quantitatively imaging static magnetic and electric potentials and even strain electron holography is a very versatile and powerful TEM technique. In this paper we compare off-axis electron holography with a recently developed focal series reconstruction algorithm and phase retrieval based on the transport of intensity equation. Based on theoretical considerations and simulations we compare the different techniques with respect to parameters such as the coherence requirements, field of view, resolution, noise properties, and other required experimental conditions.

Using dynamically scattered electrons for three-dimensional potential reconstruction

Three-dimensional charge-density maps computed by first-principles methods provide information about atom positions and the bonds between them, data which are particularly valuable when trying to understand the properties of point defects, dislocations and interfaces. This paper presents a method by which three-dimensional maps of the electrostatic potential, related to the charge-density map by the Poisson equation, can be obtained experimentally at 1 A resolution or better, especially at low accelerating voltages. The method requires data acquired by holographic transmission electron microscopy methods such as off-axis electron holography or focal series reconstruction for slightly (e.g. +/-2 degrees) different directions of the incident electron beam. The reconstruction of the three-dimensional electrostatic (and absorptive) potential is achieved by making use of changes in the dynamical scattering within the sample as the direction of the incident beam varies.

FePt Icosahedra with Magnetic Cores and Catalytic Shells

Surprisingly oxidation resistant icosahedral FePt nanoparticles showing hard-magnetic properties have been fabricated by an inert-gas condensation method with in-flight annealing. High-resolution transmission electron microscopy (HRTEM) images with sub-Angstrom resolution of the nanoparticle have been obtained with focal series reconstruction, revealing noncrystalline nature of the nanoparticle. Digital dark-field method combined with structure reconstruction as well as HRTEM simulations reveal that these nanoparticles have icosahedral structure with shell periodicity. Localized lattice relaxations have been studied by extracting the position of individual atomic columns with a precision of about ±0.002 nm. The lattice spacings of (111) planes from the surface region to the center of the icosahedra are found to decrease exponentially with shell numbers. Computational studies and energy-filtered transmission electron microscopy analyses suggest that a Pt-enriched surface layer is energetically favored and that site-specific vacancies are formed at the edges of facettes, which was experimentally observed. The presence of the Pt-enriched shell around an Fe/Pt core explains the environmental stability of the magnetic icosahedra and strongly reduces the exchange coupling between neighboring particles, thereby possibly providing the highest packing density for future magnetic storage media based on FePt nanoparticles.

Quantitative Characterization of the Interface Between a V2O3 Layer and Cu3Au (001) by Cs Corrected HREM

AbstractVanadium oxides are materials of interest due to their electronic, magnetic and catalytic properties. In the case of V2O3 and Cu3Au, the interfacial bonding is rather difficult to describe since the two component materials have strongly different electronic structures. Thus a local investigation of the interface becomes important. In this investigation, the incoherent interface between a V2O3 (0001, corundum structure) layer and a Cu3Au (001, L12 structure) substrate is characterized with the help of image corrected high resolution electron microscopy (HRTEM) and focal series reconstruction in order to investigated both the true position of atoms and the nature of the atomic species. Semi-quantitative results can be shown for the chemical composition of columns and strains at one side of the interface.

Compositional analysis of mixed–cation‐anion III–V semiconductor interfaces using phase retrieval high‐resolution transmission electron microscopy

Employing exit-plane wave function (EPWF) reconstruction in high-resolution transmission electron microscopy (HRTEM), we have developed an approach to atomic scale compositional analysis of III-V semiconductor interfaces, especially suitable for analyzing quaternary heterostructures with intermixing in both cation and anion sub-lattices. Specifically, we use the focal-series reconstruction technique, which retrieves the complex-valued EPWF from a thru-focus series of HRTEM images. A study of interfaces in Al(0.4)Ga(0.6)As-GaAs and In(0.25)Ga(0.75)Sb-InAs heterostructures using focal-series reconstruction shows that change in chemical composition along individual atomic columns across an interface is discernible in the phase image of the reconstructed EPWF. To extract the interface composition profiles along the cation and anion sub-lattices, quantitative analysis of the phase image is performed using factorial analysis of correspondence. This enabled independent quantification of changes in the In-Ga and As-Sb contents across ultra-thin interfacial regions (approximately 0.6 nm wide) with true atomic resolution, in the In(0.25)Ga(0.75)Sb-InAs heterostructure. The validity of the method is demonstrated by analyzing simulated HRTEM images of an InAs-GaSb-InAs model structure with abrupt and graded interfaces. Our approach is general, permitting atomic-level compositional analysis of heterostructures with two species per sub-lattice, hitherto unfeasible with existing HRTEM methods.

Layer Resolved Structural Relaxation at the Surface of Magnetic FePt Icosahedral Nanoparticles

The periodic shell structure and surface reconstruction of metallic FePt nanoparticles with icosahedral structure has been quantitatively studied by high-resolution transmission electron microscopy with focal series reconstruction with sub-angstrom resolution. The icosahedral FePt nanoparticles fabricated by the gas phase condensation technique in vacuum have been found to be surprisingly oxidation resistant and stable under electron beam irradiation. We find the lattice spacing of (111) planes in the surface region to be size dependent and to expand by as much as 9% with respect to the bulk value of Fe52Pt48. Controlled removal of the (111) surface layers in situ results in a similar outward relaxation of the new surface layer. This unusually large layerwise outward relaxation is discussed in terms of preferential Pt segregation to the surface forming a Pt enriched shell around a Fe-rich Fe/Pt core.

Development of Aberration-Corrected Electron Microscopy

The successful correction of spherical aberration is an exciting and revolutionary development for the whole field of electron microscopy. Image interpretability can be extended out to sub-Angstrom levels, thereby creating many novel opportunities for materials characterization. Correction of lens aberrations involves either direct (online) hardware attachments in fixed-beam or scanning TEM or indirect (off-line) software processing using either off-axis electron holography or focal-series reconstruction. This review traces some of the important steps along the path to realizing aberration correction, including early attempts with hardware correctors, the development of online microscope control, and methods for accurate measurement of aberrations. Recent developments and some initial applications of aberration-corrected electron microscopy using these different approaches are surveyed. Finally, future prospects and problems are briefly discussed.