Convergent Beam Electron Diffraction Patterns Research Articles

Crystal structure and defects visualization of Cu2ZnSnS4 nanoparticles employing transmission electron microscopy and electron diffraction

A detailed analysis of the structure of Cu2ZnSnS4 (CZTS) nanocrystals synthesized by hot-injection in the presence of oleylamine is provided employing high resolution TEM, selected area electron diffraction (SAED) and convergent beam electron diffraction (CBED). The nanostructures were investigated as-grown and after vacuum thermal treatment at 550°C. As-grown materials consisted of polycrystalline particles with an average size of 7±3nm, which grow an average size of 53±13nm after the vacuum annealing step. This thermal treatment allows investigating the initial stages of high quality film growth required in photovoltaic devices. Sets of SAED and CBED patterns, where individual crystals after annealing were viewed down different prominent zone axes, enabled us to reveal the presence of weak reflections due to cation ordering, and confirm a tetragonal unit cell consistent with either the kesterite or stannite structure. We demonstrate how these approaches enable to distinguish CZTS from secondary phases such as ZnS. Structure defects of partially annealed CZTS crystals were also investigated using bright and dark field images taken in 2-beam diffraction conditions as well as by high resolution lattice imaging. The material exhibited dislocations, along with lamellar twins and stacking faults characterized by local hexagonal structure on {112} planes. High resolution TEM images showed preferential growth on {112} planes during vacuum annealing, which is consistent with X-ray diffraction patterns. These studies provide key information on nanoscale crystal defects which may have important consequence on the performance of CZTS photovoltaic devices.

Development of splitting convergent beam electron diffraction (SCBED)

Using a combination of condenser electrostatic biprism with dedicated electron optic conditions for sample illumination, we were able to split a convergent beam electron probe focused on the sample in two half focused probes without introducing any tilt between them. As a consequence, a combined convergent beam electron diffraction pattern is obtained in the back focal plane of the objective lens arising from two different sample areas, which could be analyzed in a single pattern. This splitting convergent beam electron diffraction (SCBED) pattern has been tested first on a well-characterized test sample of Si/SiGe multilayers epitaxially grown on a Si substrate. The SCBED pattern contains information from the strained area, which exhibits HOLZ lines broadening induced by surface relaxation, with fine HOLZ lines observed in the unstrained reference part of the sample. These patterns have been analyzed quantitatively using both parts of the SCBED transmitted disk. The fine HOLZ line positions are used to determine the precise acceleration voltage of the microscope while the perturbed HOLZ rocking curves in the stained area are compared to dynamical simulated ones. The combination of these two information leads to a precise evaluation of the sample strain state. Finally, several SCBED setups are proposed to tackle fundamental physics questions as well as applied materials science ones and demonstrate how SCBED has the potential to greatly expand the range of applications of electron diffraction and electron holography.

Quantitative symmetry determination and symmetry mapping using convergent beam electron diffraction technique

The symmetry recorded in convergent beam electron diffraction (CBED) patterns is in general determined by direct visual inspection [1], which does not provide uniform measurement. Furthermore, experimental CBED patterns are often noisy and deviate from the ideal symmetry because of the sample geometry and defects. Thus, the imperfection in experimental CBED patterns can lead to uncertainty in the symmetry determination [2]. Here, we propose a symmetry quantification method for CBED patterns using the profile R-factor (Rp) [3, 4] and the normalized cross-correlation coefficient (γ) [5]. We have also developed computer algorithms to automate these procedures. We demonstrate that the method proposed here is highly effective and provides a more precise way to determine the symmetry in CBED patterns. The symmetry quantification method can be also combined with a scanning electron diffraction technique for symmetry mapping [6]. Figure 1 shows the image processing procedures for mirror symmetry quantification. First, the symmetry related two diffraction discs (A, A’) are selected about the mirror plane (yellow line) as shown in Fig. 1(a). The template A is used as the reference motif so that the symmetry element is calculated by comparing with template A’. The template A and A’ are first aligned (Fig. 1(c)), and A’ is flipped horizontally to obtain a mirror image (A’m, Fig. 1(h)). For the rotational operation, the template A’ is simply rotated by 360/no with respect to n-fold rotation. The circular mask (Figs. 1(d) and (i)) is finally used to remove areas affected by CBED disk edge and to obtain the final templates (Figs. 1(e) and (j)). Then, we applied the profile R-factor (Rp) and the normalized cross-correlation coefficient (γ) to quantify the similarity between A (=IA(x, y)) and A’m (=IB(x, y)) as given in Eqs. (1) and (2).

Quantitative STEM normalisation: The importance of the electron flux

Annular dark-field (ADF) scanning transmission electron microscopy (STEM) has become widely used in quantitative studies based on the opportunity to directly compare experimental and simulated images. This comparison merely requires the experimental data to be normalised and expressed in units of ‘fractional beam-current’. However, inhomogeneities in the response of electron detectors can complicate this normalisation. The quantification procedure becomes both experiment and instrument specific, requiring new simulations for the particular response of each instrument's detector, and for every camera-length used. This not only impedes the comparison between different instruments and research groups, but can also be computationally very time consuming. Furthermore, not all image simulation methods allow for the inclusion of an inhomogeneous detector response. In this work, we propose an alternative method for normalising experimental data in order to compare these with simulations that consider a homogeneous detector response. To achieve this, we determine the electron flux distribution reaching the detector by means of a camera-length series or a so-called atomic column cross-section averaged convergent beam electron diffraction (XSACBED) pattern. The result is then used to determine the relative weighting of the detector response. Here we show that the results obtained by this new electron flux weighted (EFW) method are comparable to the currently used method, while considerably simplifying the needed simulation libraries. The proposed method also allows one to obtain a metric that describes the quality of the detector response in comparison with the ‘ideal’ detector response.

Quantifying mean inner potential of ZnO nanowires by off-axis electron holography

Off-axis electron holography has been used to quantitatively determine the mean inner potential of ZnO. [0001] grown ZnO nanowires with hexagonal cross-sections were chosen as our samples because the angle between the adjacent surfaces is 120°, as confirmed by electron tomography, so the entire geometry of the nanowire could be precisely determined. The acceleration voltage of the transmission electron microscope was accurately calibrated by convergent beam electron diffraction (CBED)–higher-order Laue-zone (HOLZ) analyses. ZnO nanowires were tilted away from zone-axis to avoid strong dynamical diffraction effect, and the tilting angles were determined by CBED patterns. Our experimental data found a mean inner potential of ZnO as 14.30±0.28V.

FDES, a GPU-based multislice algorithm with increased efficiency of the computation of the projected potential

While the computational complexity of calculation of the projected potential in the multislice algorithm through reciprocal space scales quadratically with the number of atoms A per slice, a pure real-space calculation scales linearly with A. A hybrid strategy is introduced that has a theoretical complexity of O(AlogA), but that, when measured, outperforms both the reciprocal-space and the real-space approach by approximately an order in A and a large factor, respectively.This strategy is implemented in a new program, dubbed forward dynamical electron scattering (FDES), which simulates high resolution transmission electron microscopy images, diffraction patterns and convergent beam electron diffraction patterns. FDES attains a further increase in speed by running on a graphics processing unit and is made available to the community as open software.

Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction

Measurement of lattice strain is important to characterize semiconductor nanostructures. As strain has large influence on the electronic band structure, methods for the measurement of strain with high precision, accuracy and spatial resolution in a large field of view are mandatory. In this paper we present a theoretical study of precision and accuracy of measurement of strain by convergent nano-beam electron diffraction. It is found that the accuracy of the evaluation suffers from halos in the diffraction pattern caused by a variation of strain within the area covered by the focussed electron beam. This effect, which is expected to be strong at sharp interfaces between materials with different lattice plane distances, will be discussed for convergent-beam electron diffraction patterns using a conventional probe and for patterns formed by a precessing electron beam. Furthermore, we discuss approaches to optimize the accuracy of strain measured at interfaces. The study is based on the evaluation of diffraction patterns simulated for different realistic structures that have been investigated experimentally in former publications. These simulations account for thermal diffuse scattering using the frozen-lattice approach and the modulation-transfer function of the image-recording system. The influence of Poisson noise is also investigated.

Appropriate zone-axis orientations for the determination of crystal polarity by convergent-beam electron diffraction

A convergent-beam electron diffraction (CBED) method is proposed for polarity determination, in which polarity is determined from the intensity asymmetry of any of the hkl–\overline h\overline k\overline l Friedel pairs appearing in a zone-axis CBED pattern with a symmetric arrangement of Bijvoet pairs of reflections. The intensity asymmetry occurs as a result of multiple scattering among Bijvoet pairs of reflections in the CBED pattern. The appropriate zone-axis orientations for polarity determination are deduced for 19 of the 25 polar point groups from symmetry considerations so as to observe Bijvoet pairs of reflections symmetrically in a single CBED pattern. These appropriate zone-axis orientations deduced for the 19 polar point groups coincide with nonpolar directions. This is because the nonpolar directions for these point groups are perpendicular to an even-fold rotation axis, which guarantees the symmetric arrangement of Bijvoet pairs of reflections with respect to the symmetry (m–m′) line in a CBED pattern taken along any of the appropriate zone-axis orientations. The m–m′ line in the CBED pattern is proved to be perpendicular to the trace of the even-fold rotation axis. On the other hand, if the nonpolar direction is either perpendicular to a mirror plane or parallel to a roto-inversion axis as in the four point groups m, 3m1, 31m, \overline 6, the nonpolar direction cannot be used as the appropriate zone-axis orientation for polarity determination because the Bijvoet pairs of reflections are not arranged symmetrically in the CBED pattern. The validity of the CBED method is confirmed both by experiment and by calculation of CBED patterns.

Towards a full retrieval of the deformation tensor F using convergent beam electron diffraction

A new method to retrieve the local lattice parameters and rotations in a crystal from off-axis convergent beam electron diffraction (CBED) patterns is presented and validated using Bloch wave dynamical simulations. The originality of the method is to use both the diffracted and transmitted beams and to use kinematical approximations in the fitting algorithm. The study is based on the deformation gradient tensor F which includes rotation and strain. Working on simulated images it is shown that (i) from a single direction of observation, seven parameters out of the nine parameters of F can be determined with an accuracy of 3×10−4 for the normal strain parameters εxx, εyy, and εzz, (ii) the unit cell volume can only be retrieved if the diffracted and transmitted beams are both included in the fitting and (iii) all the nine parameters of F can be determined by combining two directions of observation separated by about 20°.

Automated CBED processing: Sample thickness estimation based on analysis of zone-axis CBED pattern

An automated processing of convergent beam electron diffraction (CBED) patterns is presented. The proposed methods are used in an automated tool for estimating the thickness of transmission electron microscopy (TEM) samples by matching an experimental zone-axis CBED pattern with a series of patterns simulated for known thicknesses. The proposed tool detects CBED disks, localizes a pattern in detected disks and unifies the coordinate system of the experimental pattern with the simulated one. The experimental pattern is then compared disk-by-disk with a series of simulated patterns each corresponding to different known thicknesses. The thickness of the most similar simulated pattern is then taken as the thickness estimate. The tool was tested on [0 1 1] Si, [0 1 0] α-Ti and [0 1 1] α-Ti samples prepared using different techniques. Results of the presented approach were compared with thickness estimates based on analysis of CBED patterns in two beam conditions. The mean difference between these two methods was 4.1% for the FIB-prepared silicon samples, 5.2% for the electro-chemically polished titanium and 7.9% for Ar(+) ion-polished titanium. The proposed techniques can also be employed in other established CBED analyses. Apart from the thickness estimation, it can potentially be used to quantify lattice deformation, structure factors, symmetry, defects or extinction distance.

Holes drilling in gold and silver decahedral nanoparticles by the convergent beam electron diffraction electron beam

The 200 kV focused electron beam in the convergent beam electron diffraction patterns mode in a transmission electron microscope (TEM) with field emission gun is able to drill holes in gold and silver decahedral nanoparticles. However, although they are done under the same circumstances, the holes are shapeless in the silver and faceted in gold nanoparticles. In addition to this, the holes are closed during their high-resolution TEM observation in both materials. To comment their differences, displacement energy considerations are taken into account as function of the sputtering energy in order to modify the displacement cross-section of the processes.

Convergent-beam electron-diffraction-pattern symmetry of nanodomains in complex lead-based perovskite crystals

Convergent-beam electron diffraction (CBED) recorded using nanometre-sized probes, in principle, can detect the highest symmetry in a crystal. However, symmetry reduction may occur by overlapping crystal domains along the beam direction. Thus, delineating the relationship between the recorded and the crystal symmetry is important for studying crystals with complex nanodomains. This paper reports a study of the averaged local symmetry of 71°/109° rhombohedral (R), 90° tetragonal (T) and 180° monoclinic (M) nanodomain structures. The averaged symmetry of nanodomain structures is investigated by CBED simulations using the multislice method. The simulation results show that the 71°-R, 109°-R and 90°-T nanodomain structures partially mimic the monoclinic symmetries ofCmandPmthat have been proposed by the adaptive phase model. This study is also compared to the reported experimental CBED patterns recorded from PMN-31%PT.

A Convergence of Beauty and Utility

The effective routine achievement of useful convergent beam electron diffraction (CBED) patterns was frustrated for many years until transmission electron microscopes (TEMs) were developed that overcame the practical difficulties. Because specimen thickness and orientation are two critical parameters in electron diffraction and are not under good control because of the difficulty of producing thin enough regions it was necessary to have TEMs capable of forming small focussed probes of less than 100nm diameter in local environments where the hydrocarbon level was sufficiently low to reduce carbon contamination to a reasonable level. Once these problems were overcome the importance of three-dimensional diffraction became apparent but to exploit this property it was necessary to develop TEMs with a large angular range in the diffraction plane. With appropriately designed instruments very beautiful CBED patterns could be obtained from crystalline samples and a variety of experimental techniques were exploited to extract meaningful information from them.

Local atomic structure determination using focused electron beams

This talk will give an overview of methods for solving the atomic structure of nanostructured materials using focused electron beams. It will illustrate these methods with a range of applications, such as the determination of the atomic structure and stability of nanoparticle facets [1]; the local atomic structure of "chessboard' nanostructures in lithium-based titanate perovskites; and the measurement of local polarity, dopant concentration and atomic-scale morphology in semiconducting nanowire quantum wells. These methods take advantage of the fact that electron wavefields can be brought to a focal point smaller than an Ångström in diameter, enabling small volumes of matter to be probed and characterized. The wealth of information contained in the resulting diffraction patterns can be interrogated selectively to isolate and `image' specific structural information. Several methods using small focused electron beams will be described in this talk, including; (i) An approach for the determination of centrosymmetric structures from the direct observation of structure factor phases by inspection of features in convergent beam electron diffraction patterns [2]. The method can achieve high resolution from just a few phase observations and no intensity measurements or iterative refinements are required; (ii) Methods for the quantitative interpretation of the intensity in atomic resolution imaging and diffraction data for the measurement of local atomic and electronic structure; (iii) Pseudo-confocal scanning transmission electron microscopy methods for obtaining depth and chemical information which record the scattered intensity in a plane conjugate to the specimen (as opposed to the diffraction plane) [3].

Extracting Local Crystallographic Structure Using 4D-STEM Datasets

Traditional scanning transmission electron microscopy (STEM) detectors are monolithic and integrate a subset of the transmitted electron beam signal scattered from each electron probe position. These convergent beam electron diffraction patterns (CBED) are extremely rich in information, containing localized information on sample structure, composition, phonon spectra, three-dimensional defect crystallography and more. Many new imaging modes become possible if the full CBED pattern is recorded at many probe positions with millisecond dwell times. In this study, we have used a Gatan K2-IS direct electron detection camera installed on an uncorrected FEI Titan-class transmission electron microscope to record 4D-STEM probe diffraction patterns on a variety of samples at up to 1600 frames per second. As an example, a 4D-STEM dataset for a multilayer stack of epitaxial SrTiO3 and mixed LaMnO3-SrTiO3 is plotted in Figure 1. Figure 1A shows a HAADF micrograph of the multilayer along a (001) zone axis. Only the A sites (Sr and La) are visible in this micrograph and the composition can be roughly determined from the relative brightness. One possible 4D-STEM technique is position-averaged convergent beam electron diffraction (PACBED) described by LeBeau et al. [1]. We can easily construct ideal PACBED patterns by averaging the probe images over each unit cell fitted from Figure 1A, which is shown in Figure 1B. By matching these patterns to PACBED images simulated with the multislice method we can precisely determine parameters such as sample thickness and composition, the latter of which is plotted in Figure 1C. For comparison, the composition has also been determined with electron energy loss spectroscopy (EELS) in a separate experiment, shown in Figure 1D. The composition range of 0-85% LaMnO3 measured by PACBED is in good agreement with the EELS measurements. In this talk we will demonstrate several other possible uses for 4D-STEM datasets.

Structure factor measurement by 3-beam convergent beam electron diffraction

It has been shown mathematically that both the magnitudes and 3-phase invariants of the structure factors of a centrosymmetric crystal can be expressed explicitly in terms of the distances to specific features in the 3-beam convergent beam electron diffraction (CBED) pattern [1].This theoretical inversion can be implemented experimentally, enabling direct observations of 3-phase invariants and the approximate measurement of structure factor magnitudes. This method then enables a different approach to crystal structure determination, which is based on the observation of phases, rather than the measurement of amplitudes. It has been shown that by inspection of just a few phases using 3-beam CBED patterns, centrosymmetric crystal structures can be determined directly to picometre precision without the need to measure magnitudes [2]. Here, we will explore a different approach for measuring structure factor magnitudes from 3-beam CBED patterns. It has been demonstrated that the relative structure factor magnitudes can be determined directly from the ratio of the intensity distributions along specific lines within the CBED discs [3]. We will investigate the potential of using this approach for the relatively fast measurement of approximate structure factor magnitudes from nano-scale volumes of crystals.

Third-dimension information retrieval from a single convergent-beam transmission electron diffraction pattern using an artificial neural network

We have reconstructed third-dimension specimen information from convergent-beam electron diffraction (CBED) patterns simulated using the stacked-Bloch-wave method. By reformulating the stacked-Bloch-wave formalism as an artificial neural network and optimizing with resilient back propagation, we demonstrate specimen orientation reconstructions with depth resolutions down to 5 nm. To show our algorithm's ability to analyze realistic data, we also discuss and demonstrate our algorithm reconstructing from noisy data and using a limited number of CBED disks. Applicability of this reconstruction algorithm to other specimen parameters is discussed.

Evidence of noncentrosymmetry of human tooth hydroxyapatite crystals.

Herein, we investigate human single hydroxyapatite crystals (enamel and dentine) by convergent-beam electron diffraction (CBED) and automated electron-diffraction tomography (ADT). The CBED pattern shows the absence of the mirror plane perpendicular to the c axis leading to the P63 space group instead of the P63 /m space group considered for larger-scale crystals, this is confirmed by ADT. This experimental evidence is of prime importance for understanding the morphogenesis and the architectural organization of calcified tissues.

Synchrotron X-ray powder diffraction and convergent beam electron diffraction studies on the cubic phase of MgV2O4 spinel

The A V2O4 (A=Mg2+, Zn2+, Cd2+) spinels are three-dimensional spin-1 frustrated systems with orbital degree of freedom, which have been known to possess intriguing orbital states causing releases of spin frustration at low temperatures. We have performed synchrotron X-ray and convergent beam electron diffraction measurements for one of these vanadates, MgV2O4 in order to clarify its crystal structure in the high temperature cubic phase, which is regarded as an important starting point for understanding the details of the low temperature phase. We have successfully observed that the [001] zone axis convergent beam electron diffraction pattern exhibits 4mm symmetry, suggesting the space group of Fd3¯m in the cubic MgV2O4. It has also been demonstrated that the crystal structure of the cubic MgV2O4 contains VO6 octahedra elongated along the threefold rotation axis. Based on our results, we discuss the orbital states of MgV2O4 as well as the other spinel vanadates.

Synthesis and Surface-Enhanced Raman Scattering Property of Pentagonal Dodecahedral Au Nanocrystals

The controlled synthesis of polyhedral Au nanocrystals (NCs) has attracted tremendous research interest in the past decades due to their promising applications in a variety of fields, such as plasmonics, sensors, electronics, catalysis, and surface-enhanced Raman scattering (SERS). Since the inherent plasmonic, electrical, and catalytic properties of Au NCs can be finely tuned by control over their shapes, numerous synthesis methods have been developed for the production polyhedral Au NCs with tailored morphologies, such as Platonic solids (tetrahedron, cube, octahedron, and icosahedron), cuboctahedron, decahedron, rod, and plate. To minimize the surface energy during the NC growth, these Au NCs are mostly enclosed by stable low-index {111} and/ or {100} facets. Recently, the synthesis of Au NCs with exposed high-energy facets, i.e., low-index {110} and highindex {hkl} (at least one index greater than 1), has been reported. NCs bound by high-energy facets have shown enhanced performance compared to conventional {111} and/ or {100}-faceted NCs due to the presence of high-density undercoordinated atoms on their surfaces as well as to their unique morphological characteristics. For instance, we reported that rhombic dodecahedral (RD) and hexoctahedral Au NCs exclusively bound by {110} and {321} facets, respectively, exhibited pronounced SERS activities. Nevertheless, it is still a great challenge to synthesize shapecontrolled NCs that are enclosed by high-index facets due to their high surface energy. Here we report for the first time on the synthesis of pentagonal dodecahedral (PD) Au NCs bound by high-index {hk0} facets. The PD Au NCs could be readily prepared by the reduction of Au precursors with N,N-dimethylformamide (DMF) in the presence of poly(vinyl pyrrolidone) (PVP). The pentagonal dodecahedron is a convex polyhedron with 12 pentagonal faces, where 3 faces meet at each corner. The surface facets of PD structures have been determined to be high-index {hk0}: the simplest one is {210} and other types are {320}, {410}, and {120}. The pentagonal dodecahedron has been known as a very unusual structure and crystalline materials with this structure have been rarely reported. Only the crystal of pyrite and some quasi crystals have this structure. To the best of our knowledge, the synthesis of metal NCs with PD structure has never been reported. Furthermore, the prepared PD Au NCs could be successfully applied in the field of SERS. Highly enhanced SERS signals could be obtained from various analytes with the PD Au NCs, which can be attributed to their high-surface energy facets. Figure 1(a) and (b) show representative lowand highmagnification field-emission scanning electron microscopy (FESEM) images of the as-prepared samples, demonstrating the formation of Au NCs with a well-defined structure. The sizes of Au NCs were in the range of 150-200 nm. The SEM image of NCs, shown in Figure 1(b), is closely matched by the 3D models of dodecahedra with different orientations (Figure 1(c)), indicating the successful generation of PD Au NCs enclosed by 12 pentagons under our experimental conditions. The X-ray diffraction (XRD) pattern of the PD Au NCs showed distinct diffraction peaks from the face centered cubic (fcc) structure of Au, revealing their crystalline nature (Figure 1(d)). Figure 2(a) shows the transmission electron microscopy (TEM) image of a PD Au NC recorded along the [110] direction. The corresponding convergent beam electron diffraction (CBED) pattern is also shown in Figure 2(b), which