Convergent-beam Electron Diffraction Discs Research Articles

Direct observation of rotation of polarization at 90-degree domain walls in BaTiO3

The rotation of polarization at 90-degree domain walls in tetragonal BaTiO3 was directly observed by the STEM-CBED method, which combines scanning transmission electron microscopy and convergent-beam electron diffraction (CBED). The CBED patterns in the domain wall region exhibit continuous changes in intensity distribution within disks and specific features corresponding to the direction of the rotation of polarization. Simulations were performed using hypothetical superstructures created by continuously connecting Ti displacement with a 90-degree rotation and showed good qualitative agreement with the experimental patterns. The quantitative evaluation of the mirror symmetries existing in the tetragonal structure in bulk form revealed the width of the domain wall is approximately 9 nm. While distorted regions with slightly broken symmetry in CBED disks were found to extend further on both sides of the domain wall region in 6–7 nm. This finding can explain the discrepancy in the domain wall widths reported in previous studies.

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).

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.

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.

Structural Analysis of Fluorine-Free Oxypnictide Superconductor NdFeAsO1-y by Electron Diffraction Analysis and Electron Microscopy

The discovery of the iron-based oxypnictide superconductor LaFeAsO1 xFx has reinvigorated research on superconductors, and has been quickly followed by a number of studies of a series of lanthanide iron-based oxypnictide superconductors. Of these oxypnictide superconductors, SmFeAsO1 xFx exhibits the highest critical temperature (Tc) of 55K. Charge doping from reservoir layers consisting of LnO1 xFx (Ln: lanthanide) to conduction layers consisting of FeAs, is considered to be controlled by the substitution of oxygen atoms with fluorine atoms. Although there have been discussions comparing the superconducting properties of iron-based oxypnictides and copper-based oxide superconductors, experimental data for new oxypnictide superconductors remain relatively scarce. Recently, Kito et al. have succeeded in preparing a series of fluorine-free lanthanide iron-based oxypnictide superconductors by a high-pressure technique. Carrier doping is controlled in this case by oxygen vacancies formation instead of fluorine replacement. The crystallographic structures of such fluorine-free iron-based oxypnictide superconductors, and particularly the order or disorder of oxygen vacancies, should thus be investigated. In this short note, the crystallographic structure of NdFeAsO1 y (1 y 1⁄4 0:5 nominal) with Tc 1⁄4 54K, synthesized by a high-pressure technique, is evaluated by electron diffraction analyis and electron microscopy. The space group thus elucidated has assisted subsequent quantitative structural analysis by Rietveld neutron diffractometry. NdFeAsO0:5 specimens for microscopy observation were prepared by argon-ion milling. Transmission electron microscopy (TEM) was performed using JEM 4000FX and JEM2010 instruments at 200 kV. The present samples were polycrystalline with a grain size of several hundreds of nanometers. No other phases could be clearly detected, although some lattice defects were observed. Figure 1 shows the electron diffraction pattern of the material taken on the [001] zone axis. No intensity of diffuse scattering due to the short-range ordering of oxygen vacancies is observed. However, very weak spot intensities are visible in the diffraction pattern taken over a longer exposure period, as indicated by arrows in the figure. These spot intensities correspond to positions hk0; hþ k 1⁄4 2nþ 1, and might indicate the long-range ordering of oxygen vacancies. Figure 2 shows an electron diffraction pattern taken on the [100] zone axis. Strong diffraction spots are apparent at 0k0; k 1⁄4 2nþ 1 in this case. Figure 3 shows the convergent beam electron diffraction (CBED) pattern observed on the [100] zone axis. Gjonnes–Moodie lines appear in the CBED discs at 0k0; k 1⁄4 2nþ 1. The diffraction intensity at 0k0; k 1⁄4 2nþ 1 and the weak spot intensities in Fig. 1 are thus considered to be due to multiple scattering. No other extra reflections caused by the long-range ordering or diffuse scattering due to the short-range ordering of vacancies are observed. Oxygen vacancies are concluded to be in a disordered state. No diffracted intensity associated with vacancy ordering is also observed in powder neutron diffraction measurement. The observation of electron diffraction spots corresponding to the 0th-order Laue zone and the firstorder Laue zone on the [001] zone axis indicates that the extinction rule is hk0 with hþ k 1⁄4 2n, suggesting the space group P4=n (No. 85) or P4=nmm (No. 129) for this crystal. P4=n has a fourfold rotational axis about the [001] zone axis, while P4=nmm has a 4mm symmetry around the Fig. 1. Electron diffraction pattern on the [001] zone axis. Weak spot diffractions are indicated by white arrows.

On the peculiarities of CBED pattern formation revealed by multislice simulation

A modified multislice method has been developed for calculations of Convergent Beam Electron Diffraction (CBED) patterns. The validity of the method for HOLZ- and Kikuchi-line calculations has been proofed by comparison to Bloch-wave calculations. The application of the method leads to the new understanding of CBED patterns formation. Dynamical scattering of weak HOLZ reflections plays the key role in the appearance of deficient lines in the central CBED disk. Different HOLZ lines do have significantly different and extended scattering areas; the central 000 CBED disk, consequently, contains structural information from an area around the primary beam which is determined by the Bragg angle of HOLZ reflections and the thickness of the sample. A variation of lattice parameters, if present within this area, results in artificial symmetry violations of the pattern and in changes of line profiles.

Low-Dose, Low-Temperature Convergent-Beam Electron Diffraction and Multiwavelength Analysis of Hydrocarbon Films by Electron Diffraction

Aromatic hydrocarbon (perylene, coronene) and tetracontane films are shown to produce useful convergent-beam electron diffraction (CBED) patterns under low-dose and low-temperature conditions. These were obtained using a Zeiss LEO-921 electron microscope with an omega energy filter at liquid helium and nitrogen temperatures. The usefulness of patterns showing CBED disks of constant intensity ("blank disks," indicating kinematic scattering) for structure analysis is investigated, with the aim of avoiding film-bending artifacts. Using CBED patterns from thicker areas, sample thickness was experimentally determined using either two-beam or three-beam patterns. Koehler mode illumination (a new form of SAD pattern offering smaller areas) was also used, and the possibility of obtaining structure factor moduli using the kinematic and two-beam approximations was investigated by comparing measured diffraction intensities with experimental ones for these known structures. The commonly used approximation [F] approximately I(g) (intended to account for bending) was found to be a worse approximation than the two-beam approximation with well-defined excitation error for these microdiffraction experiments. A new multiwavelength method of retrieving structure factor moduli and thickness from microdiffraction patterns using two-beam theory is demonstrated for tetracontane.

Kinematic and dynamical CBED for solving thin organic films at low temperature; experimental tests with anthracene.

Low-dose, low-temperature kinematic and dynamical convergent-beam electron diffraction (CBED) patterns from thin organic crystalline films have been used for the measurement of structure-factor amplitudes and phases. Kinematic conditions are identified by the observation of uniform intensity within the CBED discs and used to determine structure-factor magnitudes. CBED patterns from thicker regions affected by multiple scattering give structure-factor signs, which are varied for best fit. The use of a small probe (and the Kohler SAD mode) minimizes bending artifacts. A new method of thickness determination is evaluated. The approach is tested using experimental data from the centrosymmetric anthracene structure, the results compared with direct methods, and a potential map derived from experimental data. The faint peaks due to H-atom positions may be distinguished. Key issues influencing the validity of the method such as the appropriate dimension of the structure-factor matrix, sample thickness and crystal orientation are discussed.

Lattice Strain around Platelet Oxide Precipitates in C- and N-Doped Silicon Epitaxial Wafers

The effect of heavy C and N doping on local lattice strain around platelet oxide precipitates in Czochralski silicon substrates of p/p− epitaxial (epi) wafers was investigated quantitatively using convergent beam electron diffraction (CBED). C- and N-doped p/p− epi wafers, including platelet precipitates with an edge length of approximately 500 nm, were prepared with an isothermal annealing at 800°C for 700 h. The results of strain analysis were compared with the reported results of polished wafers and heavily B-doped epi wafers, including an almost equal platelet density and length to C- and N-doped epi wafers. It was found, with strain analysis from high order Laue zone patterns in the CBED disk, that (i) the type of lattice strain in C- and N-doped epi wafers was coincided to polished and B-doped epi wafers. The strain along the normal direction to the flat plane of the platelet precipitate was compressive, while the strain along the parallel direction to the flat plane of the platelet was tensile; (ii) the strain in C-doped epi wafers was as large as that in B-doped epi wafers, and far relaxed compared with N-doped epi and polished wafers. Since the substitutional carbon concentration did not change during the isothermal annealing, the strain relaxation in C-doped epi wafers was caused by the availability of effective sinks in the matrix for silicon interstitials emitted by the precipitates. © 2001 The Electrochemical Society. All rights reserved.

Effect of heavy boron doping on the lattice strain around platelet oxide precipitates in Czochralski silicon wafers

The effect of heavy boron doping on local lattice strain around platelet oxide precipitates in Czochralski silicon wafers was investigated quantitatively by convergent beam electron diffraction (CBED). Lightly boron doped (p−) polished wafers, including platelet precipitates with density of about 5×109/cm3 and with an edge length of about 500 nm, were prepared with an isothermal annealing at 800 °C for 700 h. Heavy boron doped (p/p+) epitaxial wafers, including an almost equal precipitate density and length to p− wafers, were also prepared with an isothermal annealing at 800 °C for 200 h. It was found by strain analysis from high-order Laue zone patterns in the CBED disk that (i) the type of lattice strain was coincident in p− and p/p+ wafers: the strain along the normal direction of the platelet precipitate was compressive, while the strain along the parallel direction of the platelet was tensile; (ii) the strain in p/p+ wafers was smaller than that in p− wafers; and (iii) the punched-out dislocations were generated by platelets only in p− wafers. The results of (ii) and (iii) indicate that the strain around the platelets is relaxed due to the heavy boron doping.

Analysis of Local Lattice Strain Around Oxygen Precipitates in Czochralski-Grown Silicon Wafers Using Convergent Beam Electron Diffraction

The local lattice strain field around oxygen precipitates in Czochralski-grown silicon (CZ-Si) wafers has been measured quantitatively using convergent beam electron diffraction (CBED). As a result of the strain analysis from higher-order Laue zone patterns in the CBED disk, strain of the silicon lattices was found in the vicinity of oxygen precipitates, i.e., platelet type and polyhedral type. The strain along the normal direction to the precipitate is compressive, and the strain along the parallel direction to the precipitate is tensile. The lattice strain field around the precipitate decreases monotonically as a function of distance from the precipitate/matrix interface. Further, the morphological change in the growth process of the precipitate is important for the formation of the local lattice strain.

Microstructure Development in Laser-Processed Al–Ti–Ni Alloys with 25 At. % Ti

The microstructure of laser-processed (Al1−xNix)3 Ti with Ni content ranging from 5 to 15 at. % has been studied by scanning-and transmission-electron microscopy (SEM and TEM). All samples contain Al-rich dendrites with Ni-rich interdendritic phases. The dendrites in the 5 at. % Ni alloy consist of the Al3Ti phase with the DO22 type structure, whereas the alloys containing 8 to 15 at. % Ni consist of the Al67Ni8Ti25 phase with the L12-type structure. The lattice parameter of the L12 type structure of Al67Ni8Ti25 was determined by comparing the Higher Order Laue Zone (HOLZ) line patterns in experimental and calculated convergent beam electron diffraction disks. The lattice parameter was found to be a = 0.3935 ± 0.0003 nm. Within the L12 type regions of the alloy with 8 at. % Ni, precipitates with a new primitive tetragonal structure was found. The cell dimensions are a = 0.39 nm and c = 1.18 nm. AlNTi2 with Ti: Al ratio equal to 2.0 ± 0.2 was found as needles in interdendritic regions. The cell dimensions are consistent with a = 0.299 nm and c = 1.361 nm and space group P63/mmc.

Convergent-beam electron diffraction study of incommensurately modulated crystals. II. (3+1)-dimensional space groups

The convergent-beam electron diffraction (CBED) method for determining three-dimensional space groups is extended to the determination of the (3+1)-dimensional space groups for one-dimensional incommensurately modulated crystals. It is clarified than an approximate dynamical extinction line appears in the CBED discs of the reflections caused by an incommensurate modulation. The extinction enables the space-group determination of the (3+1)-dimensional crystals or the one-dimensional incommensurately modulated crystals. An example of the dynamical extinction line is shown using an incommensurately modulated crystal of Sr2Nb2O7. Tables of the dynamical extinction lines appearing in CBED patterns are given for all the (3 + 1)-dimensional space groups of the incommensurately modulated crystal.

Measurement of Thermally-Induced Strains in Polycrystalline Al Thin Films on Si Using Convergent Beam Electron Diffraction

ABSTRACTStrains in polycrystalline Al films grown on oxidized Si wafers were measured using convergent beam electron diffraction (CBED). CBED patterns were acquired on a Zeiss EM 912 TEM equipped with an imaging energy filter and CCD camera. HOLZ line positions in the (000) CBED disk were matched using an automated refinement procedure. A sensitivity to variations in lattice parameter of approximately 0.00007 nm was obtained. Strong deviations from a simple equibiaxial strain, perfect [111] texture model were observed.

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.

TEM study on laser processed intermetallic phases: Al16Ti6(Fe or Ni)7

The structures of two laser processed ternary intermetallic phases, Al16Ti6(Fe or Ni)7, have been studied by using electron diffraction and microscopy. A convergent beam electron diffraction (CBED) technique for structure determination is described based upon the principle of kinematic interpretation of large angle systematic reflections in CBED disks. The structure type of phases Al16Ti6(Fe or Ni)7 is characterized as the Mn23Th6(cF116)-type, the same as those of relevant phases Cu16Mg6Si7 and Al50Ti25Fe25 etc., by using the CBED technique. Various errors involved in the analyses are also discussed.

On the sign ambiguity of triplet phases in nonsystematic many-beam effects in CBED patterns

The possibility to determine not only the magnitude but also the sign of three-phase structure invariants from nonsystematic many-beam effects in convergent-beam electron diffraction (CBED) patterns is discussed. From the full dynamical many-beam intensity expression it is clear that it is a principal difference between equivalent three-beam cases of opposite sign of the triplet phases. However, the difference and thus the ability to distinguish between the two cases depends strongly both on the relative magnitude of the structure factors involved and the specimen thickness for which the actual CBED discs are obtained. The largest differences are obtained for a weakly coupled three-beam case where the intensity in the line of the primary reflection, which in this case coincides with the kinematical two-beam position, has a distinct maximum or minimum at the three-beam condition depending on the sign of the triplet phase. In a strong coupling case where the intensity in the primary-reflection line near the three-beam condition is split into two individual segments, the differences are generally less and are not so obvious and quantitative measurements are necessary to distinguish the two cases of opposite sign of the triplet phases. Calculated examples with respect to a nonsystematic three-beam example in the noncentrosymmetric InP are given.

Observation of phase contrast in covergent-beam electron diffraction patterns

A conventional transmission electron microscope equipped with a cold field emission source (Hitachi HF-2000) was used to record coherent phase contrast from the overlap regions of convergent-beam electron diffraction (CBED) patterns in 6H SiC. The focused probe size (∼ nm) was smaller than the planar spacing allong the c axis (1.5 nm). When a probe was slightly defocused to illuminate several units cells, the overlaps between adjacent CBED discs showed parallel sets of fringes, with relative shifts that were consistent with the phasing of the SiC structure factors.

Numerical evaluation of lattice parameters from high-order Laue zone lines in convergent-beam electron diffraction disks

In this paper a numerical method is reported for the evaluation of the lattice parameters of any crystal structure, without using standard samples. This method makes use of the higher-order Laue zone (HOLZ) lines present in the transmitted disk of convergent-beam electron diffraction patterns, observed under kinematical conditions. The lattice parameters are evaluated by performing the best fit of the measured and the calculated distances of the HOLZ lines from the centre of the transmitted convergent-beam diffraction disk. This method has been tested by determining the lattice parameter of a simple cubic crystal in comparison with the method based on the configuration changes of the HOLZ lines as the cell parameters is changed. In addition, the crystallographic constants of a hexagonal structure are evaluated and the effects of extended lattice defects are shown.