Zone-axis Convergent-beam Electron Diffraction Research Articles

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.

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.

Polarity determination of ferroelectric LiNbO 3 crystals and BiFeO 3 thin films by the convergent beam electron diffraction technique

The applicability of various convergent beam electron diffraction (CBED) methods to the polarity determination of LiNbO 3 crystals in the space group R3c was examined. We show that the method of zone-axis CBED combined with dynamical simulation is applicable to the polarity determination of LiNbO 3. The effects of the zone axis, the specimen thickness and the displacement of the homopolar atom on the polarity determination were studied. This method was also successfully applied to the polarity determination of a multiferroic BiFeO 3 film deposited on a (111)Pt/TiO 2/SiO 2/Si substrate by pulsed laser deposition. It shows that about 30% of the grains in the BiFeO 3 film are grown along the positive polar direction.

Quantitative and easy estimation of a crystal bending effect using low-order CBED patterns

The quantitative measurement of a crystal bending effect is performed using low-order zone-axis convergent beam electron diffraction (CBED) patterns. Although the accuracy of the present method is inferior to that of the method of using split higher order Laue zone lines, this method enables us to estimate the crystal bending effect at a region very close to the interface and to easily judge whether the crystal bending effect results in a tensile bend or a compressive bend. As an application of the present method, the crystal bending effect at a region close to the SiGe/Si interface was measured. It was found that the crystal bending effect is due to a thin-foil relaxation of almost 0.3 degrees at a region that is approximately 10 nm away from the interface.

New electron diffraction method to identify the chirality of enantiomorphic crystals.

A new CBED (convergent-beam electron diffraction) method is proposed for the identification of the chirality of enantiomorphic crystals, in which asymmetry in the intensity of the reflections of Bijvoet pairs in an experimental symmetrical zone-axis CBED pattern is compared with that of a computer-simulated CBED pattern. The intensity difference for reflections of these Bijvoet pairs results from multiple scattering (dynamical nature of electron diffraction) among relevant Bijvoet pairs of reflections, each pair of which has identical amplitude and different phase angles. Therefore, the crystal thickness where chiral identification is made with the present method is limited by the extinction distance of Bijvoet pairs of reflections relevant to multiple scattering to produce the intensity asymmetry, which is usually of the order of a few tens of nanometers. With the present method, a single CBED pattern is sufficient and chiral identification can be made for all the possible enantiomorphic crystals that are allowed to exist in crystallography.

Quantitative Zone-Axis Convergent Beam Electron Diffraction: Current Status and Future Prospects

Quantitative zone-axis convergent beam electron diffraction (CBED) is now an established technique. Over the past decade it has been developed into a tested method for the accurate refinement of structure factors, allowing the details of the charge density and bonding effects to be studied in crystalline materials. Strategies for obtaining the most accurate results have evolved, and the most important influences on the accuracy have been determined. Initial applications of the technique to bond charge density determination have led to the extension of the method to the refinement of other important parameters influencing the experimental data, such as Debye-Waller factors and the absorption potential. The development and current status of quantitative zone-axis CBED are discussed. Prospects for the future development and application of the technique are also considered.

Defect structures in TaSi 2 thin films produced by co-sputtering

Phase transformation and defect structures in thin-film TaSi 2 produced by co-sputtering have been investigated as a function of annealing temperature by transmission electron microscopy. Crystallization of amorphous TaSi 2 thin films occurs at 400 °C without forming any metastable phases. Most of C40 TaSi 2 crystallites contain planar faults parallel to (0001) basal planes. Convergent-beam electron diffraction (CBED) indicates that these planar faults are not simple stacking faults but are twin boundaries bounded by two adjacent enantiomorphically-related twin domains; i.e., domains belonging to the space groups P6 222 (right-handed) and P6 422 (left-handed) having the identical crystal orientation arrange alternatively separated by twin boundaries parallel to (0001). The formation of these enantiomorphically-related domains in TaSi 2 thin films with the hexagonal C40 structures is discussed in comparison with the formation of twin-related domains in MoSi 2 (the tetragonal C11 b structure) and TiSi 2 (the orthorhombic C54 structure) thin films. A new CBED method is proposed for identification of enantiomorphically-related crystals, in which asymmetry in the intensity of Bijvoet pairs of FOLZ disks in an experimental symmetrical zone-axis CBED pattern is compared with that in a computer simulated CBED pattern.

Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. I. Structure-factor measurements.

The zone-axis CBED pattern-matching technique ZAPMATCH [Bird & Saunders (1992). Ultramicroscopy, 45, 241-251] has been applied to low-order structure-factor measurements in nickel and copper. Considerable disagreement exists between previously published results obtained with a variety of solid-state theories and experimental techniques. The nickel ZAPMATCH results confirm previous electron-diffraction critical-voltage measurements and are in excellent agreement with FLAPW (full-potential linearized augmented plane-wave) theory calculations. This is further proof of the accuracy achievable with ZAPMATCH analysis. For copper, however, while the results support the findings of previous experimental measurements, they are consistently higher than those given by a range of solid-state theories, perhaps demonstrating some limitation in the existing theory. Two extensions to the ZAPMATCH technique are also considered. First, rules are developed to determine the number of structure factors that can be refined accurately from a given CBED pattern. Second, the imaginary potential generally introduced to account for the effects of thermal diffuse scattering (TDS) is also refined. It is shown that, while the widely used Einstein model is a useful approximation, the refined values are consistently higher than the model predicts. In addition, the importance of a second-order (real) TDS correction arising from the Einstein model is investigated. Although its effects are limited in this instance, it may prove to be more significant at lower beam energies or for materials of higher atomic number.

Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. II. Debye-Waller-factor measurements.

Quantitative CBED techniques, such as the ZAPMATCH zone-axis pattern-matching method [Bird & Saunders (1992). Ultramicroscopy, 45, 241-251], have been applied with great success to the accurate refinement of low-order structure factors. The major limitation on the accuracy of the structure-factor measurements is uncertainty in the Debye-Waller factors describing the temperature-dependent atomic vibrations. While X-ray and neutron diffraction tech-niques are both capable of accurate measurements of Debye-Waller factors, the frequent use of liquid-nitrogen-cooled samples in CBED experiments means that previous measurements are rarely available at the temperatures required. This has prompted attempts to determine Debye-Waller factors from electron diffraction data obtained under experimental conditions that match those used for the quantitative CBED work. In this paper, the possibility of extracting accurate Debye-Waller factors from the low-order reflections of a zone-axis CBED pattern is investigated. In this way, the Debye-Waller factors and structure factors could be obtained from the same data set. With this new approach, it is shown that errors lower than +/-0.02 Å(2) can be obtained for the measurement of Debye-Waller factors from room- and liquid-nitrogen-temperature nickel and copper <110> zone-axis data. The results obtained are compared with previous measurements and theoretical predictions.

Energy Filtered Imaging and Convergent Beam Electron Diffraction (CBED) in the Transmission Electron Microscope (TEM)

Over the last ten years TEMs have been developed that are capable of HREM, EDX, PEELS and diffraction using a single objective pole piece. More recently these TEMs have been equipped with the capability of energy filtering the electron beam after it has passed through the sample so that energy filtered images and electron diffraction patterns can be obtained. In this work the use of a Topcon 002B TEM equipped with a GATAN PEELS imaging filter (GIF) to generate zero-loss energy filtered zone axis CBED patterns and elemental images from inelastically scattered electrons will be described. An analysis of this energy filtered data indicates that elemental imaging using the GIF is an informative, but semiquantitative technique, whereas zero-loss energy filtered zone axis CBED patterns can be accurately quantified so that the two lowest-angle x-ray form factors of cubic elements can be measured with errors of the order of 0.1% or less.

The use of Bethe potentials in zone-axis CBED pattern matching

In recent years quantitative diffraction techniques have been developed which can obtain accurate low-order structure factors by matching theoretical calculations to experimental energy-filtered Convergent Beam Electron Diffraction (CBED) patterns. These techniques rely on the calculation of accurate diffraction intensities which requires lengthy computation. We have previously described a method of reducing computing times using perturbation theory. In this paper we describe a modification to our original zone-axis pattern matching method to include Bethe potentials. The modifications to the pattern matching process are described and the results of structure factor measurements for Si [110] patterns using Bethe potentials are discussed.

Zone-axis convergent-beam electron diffraction and ALCHEMI analysis of Ti[sbnd]Al alloys with ternary additions

Abstract A new statistical method for atom location by channelling-enhanced micro-analysis is applied to γ [sbnd] α2 duplex Ti[sbnd]Al based alloys containing ternary element additions of V, Cr, Mn, Ga, Y, Zr, Nb, Mo, La, Hf, Ta and W at the 1 at.% level. Incoherent channelling patterns, formed by the variation in characteristic X-ray emission as a function or orientation, are collected from a number of different zone axes from both phases. Comparisons of experimental patterns with calculated maps for various crystallographic sites indicate that the ternary atoms are incorporated substitutionally in the atomic structure of both the γ and the α2-phases and do not occupy interstitial sites. The crystallographic site distribution of the ternary elements is determined through χ2-minimization techniques, together with quantitative error limits. The structure of the non-stoichiometric α2-phase is investigated by convergent-beam electron diffraction.

What is the ultimate precision of CBED structure factor measurement? Application to Group IV and III-V semiconductors

We have previously demonstrated the feasibility of fitting calculated zone-axis Convergent Beam Electron Diffraction (CBED) patterns to zero-loss energy-filtered experimental data. The aim of this pattern matching procedure is to refine accurate low-order structure factors that can be used to reconstruct the bonding charge density. Initial tests on silicon [110] zone-axis patterns have shown that this new electron diffraction technique is capable of accuracies comparable with existing X-ray methods and that the results are in good agreement with solid state theory calculations. The general applicability of the CBED pattern matching technique is now investigated by studying the bond charge of two other Group IV materials, i.e. germanium and diamond, and the HI-V semiconductor GaAs.The (110) plane of the reconstructed bond charge density for each of the Group IV materials is shown in Figure 1. The agreement between these results and those predicted by solid state theory is excellent despite the use of only five independent Fourier components in the reconstruction.

Benefits of energy filtering for advanced convergent beam electron diffraction patterns

Energy filtering is well known to have a dramatic effect on the appearance of standard, zone-axis convergent beam electron diffraction patterns. In this paper, the effects of energy filtering on some less-common types of CBED patterns are shown. In particular, the (002) and (402) quasi-forbidden reflections in silicon are investigated, and the effects of energy filtering demonstrated. The filtering of HOLZ excess lines in large-angle zone-axis patterns is shown, as these patterns are of interest for Debye-Waller factor determination. Filtered and unfiltered bright-field large-angle CBED (LACBED) patterns of aluminum are presented along with EELS spectra to demonstrate the partial removal of inelastically scattered electrons due to the LACBED geometry.

Convergent-beam thickness determination: The advantages of digital imaging

Convergent-beam electron diffraction (CBED) patterns contain an immense amount of information relating to the structure of the material from which they are obtained. The analysis of these patterns has progressed to the point that under appropriate, well specified conditions, the intensity variation within the CBED discs may be understood in a quantitative sense. Rossouw et al for example, have produced numerical simulations of zone-axis CBED patterns which show remarkable agreement with experimental patterns. Spence and co-workers have obtained the structure factor parameters for lowindex reflections using the intensity variation in 2-beam CBED patterns. Both of these examples involve the use of digital data. Perhaps the most frequent use for quantitative CBED analysis is the thickness determination described by Kelly et al. This analysis has been implemented in a variety of different ways; from real-time, in-situ analysis using the microscope controls, to measurements of photographic prints with a ruler, to automated processing of digitally acquired images. The potential advantages of this latter process will be presented.

Convergent-beam electron diffraction study of modulations in semiconductor superlattices

Abstract The dependence of zone axis superlattice higher-order Laue zone (HOLZ) lines of reflections of AlAs/GaAs superlattices on the accelerating voltage of the electron microscope and the specimen thickness has been studied by conventional zone axis convergent-beam electron diffraction (CBED) and large-angle CBED Tanaka dark-field patterns. This is compared with satellite sidebands in a GeSi/Si strained-layer superlattice with a larger period of modulation. It is shown that zone axis superlattice HOLZ lines and satellite sidebands in Tanaka dark-field patterns are equivalent.

Convergent-beam electron diffraction characterization of dislocations in GaS single crystals

The effects of dislocations in GaS single crystals both on the high symmetry zone-axis convergent-beam electron diffraction patterns and on the Tanaka patterns have been studied. The dislocations induce splitting in some reflections of the low camera length diffraction patterns. The modifications have been analyzed according to the kinematical theory, so the splitting and the unsplitting of the reflections correspond to the visibility and invisibility of the defect. The Burgers vectors of the dislocations have been determined by the analysis of a single zone-axis diffraction pattern. In addition, the deformations induced by isolated dislocations in Tanaka patterns have been analyzed and the distortions have been seen to depend on the character of the observed dislocation. A quick discrimination among edge, screw and mixed dislocations has been performed by the analysis of the Tanaka pattern distortion.

Observation of Dynamic Extinction Lines in the (420) Diffraction Disks of the MgAl2O4 Spinel &lt;100&gt; CBED Pattern

Many people have observed dynamic extinction lines in the {200} diffraction disks of the &lt;100&gt; zone axis CBED (convergent beam electron diffraction) patterns of the MgAl2O4 spinel. These dark lines are manifestation of the space group of the material and can easily be explained with the Gjønnes-Moodie theory. However, in addition to the extinction lines in the {200} disks, We have also been able to observe dynamic extinction lines present in the {420} diffraction disks in the same CBED pattern.The CBED work in this work was carried out with a JEOL-2000FX microscope operated at 100.15 kV. One &lt;100&gt; zone axis CBED pattern is shown in Fig. 1. The dark lines are clearly shown in the {420} disks running through the two perpendicular non-principal axes, in exactly same way as the dark lines in {200} disks.One can easily explain the dynamic extinction lines in the {200} disks with the Gjønnes-Moodie theory by drawing dynamic scattering pairs oG-Ga and oH-Ha, oK-Ka and oL-La etc. in the diagram (Fig. 2).

Some practical aspects of CBED applications in materials science

The paper by Buxton et al. has firmly laid down the theoretical foundation for the point group determination of a crystal structure with convergent beam electron diffraction (CBED). Numerous examples of successful applications of this theory to materials science problems have been published. However, it has also been observed that, for an unambiguous determination of some crystal structures, more zone axis CBED patterns are needed than it is indicated by the tables in the paper. Yet sometimes ambiguity can still exist as in the case of the point group determination of the MgAl2O4 spinel, where CBED is unable to detect an alleged Al3+ ion displacement of Δb=0.0002∼0.0006 nm along a &lt;111&gt; direction and thus unable to determine whether its point group should be m3m or m. This difficulty might be attributed to the fact that, as for microanalysis, such as x-ray energy dispersive spectroscopy and electron energy-loss spectroscopy, the CBED technique must have its detection limit beyond which the detail in an acquired CBED pattern is not adequate enough to permit an unambiguous determination of its diffraction group.

Observation of dependent to independent Bloch wave transition in Kikuchi patterns

The transition from dependent to independent Bloch waves in high-energy electron diffraction theory is demonstrated by observing the disappearance of subsidiary fringes in Kikuchi patterns as the crystal thickness is increased. Comparison is made between experimental and computed Kikuchi band profiles in Si. It is shown that the subsidiary fringes provide a method for thickness determination in zone axis convergent-beam electron diffraction patterns from relatively thin crystals.