Convergent-beam Diffraction Patterns Research Articles

Thickness profiling of electron transparent aluminium alloy foil using convergent beam electron diffraction.

Convergent beam electron diffraction (CBED) was used to profile the thickness of aluminium alloys foils prepared by using the twinjet electropolishing method. The two-beam CBED condition was obtained by exciting the and aluminium diffracted g-vector. The aluminium alloy foil thicknesses were calculated at different distances from the sample hole edge. In areas where only one Kossel-Möllenstedt (K-M) minima fringe was obtained, the thickness was determined by matching the experimental with simulated convergent beam diffraction patterns. In areas far away from the sample edge, the thickness of foils was high enough to generate at least two (K-M) minima fringes, required for linear regression fitting.

Particle size and convergent electron diffraction patterns of triangular prismatic gold nanoparticles

Convergent beam diffraction (CBED) patterns of nanoparticles are possible. CBED of triangular prismatic shaped Au nanoparticle with focus on diffraction pattern symmetry and forbidden reflections observed along [111] and [112] zone axes are reported in this work. It is well known that the CBED patterns of nanoparticles of 30 nm or less in size only show bright kinematical discs. The dynamic contrast with Kikuchi and sharp HOLZ lines within the bright discs, as observed in CBED of volumetric materials, is well observed in particles larger of 500 nm in size. In addition, it is shown that the 1/3[422] and 1/2[311] weak forbidden reflections observed in the [111] and [112] electron diffraction patterns of these particles do not modify the symmetry of the CBED patterns, but they disappear as the size of the particle increases. The symmetry of the CBED patterns are always observed in concordance with the space group Fm3m (No. 225) of the Au unit cell. The possible explanations for observing forbidden reflections are the incomplete ABC stacking due to surface termination and the stacking faults in the fcc structure.

Expanding the Dimensions of a Small, Two-Dimensional Diffraction Detector.

We report an approach to expand the effective number of pixels available to small, two-dimensional electron detectors. To do so, we acquire subsections of a diffraction pattern that are then accurately stitched together in post-processing. Using an electron microscopy pixel array detector (EMPAD) that has only 128 × 128 pixels, we show that the field of view can be expanded while achieving high reciprocal-space sampling. Further, we highlight the need to properly account for the detector position (rotation) and the non-orthonormal diffraction shift axes to achieve an accurate reconstruction. Applying the method, we provide examples of spot and convergent beam diffraction patterns acquired with a pixelated detector.

Atomic resolution convergent beam electron diffraction analysis using convolutional neural networks

Two types of convolutional neural network (CNN) models, a discrete classification network and a continuous regression network, were trained to determine local sample thickness from convergent beam diffraction (CBED) patterns of SrTiO3 collected in a scanning transmission electron microscope (STEM) at atomic column resolution. Acquisition of atomic resolution CBED patterns for this purpose requires careful balancing of CBED feature size in pixels, acquisition speed, and detector dynamic range. The training datasets were derived from multislice simulations, which must be convolved with incoherent source broadening. Sample thicknesses were also determined using quantitative high-angle annular dark-field (HAADF) STEM images acquired simultaneously. The regression CNN performed well on sample thinner than 35 nm, with 70% of the CNN results within 1 nm of HAADF thickness, and 1.0 nm overall root mean square error between the two measurements. The classification CNN was trained for a thicknesses up to 100 nm and yielded 66% of CNN results within one classification increment of 2 nm of HAADF thickness. Our approach depends on methods from computer vision including transfer learning and image augmentation.

Atomic Resolution Convergent Beam Electron Diffraction Analysis Using Convolutional Neural Networks

Abstract Two types of convolutional neural network (CNN) models, a discrete classification network and a continuous regression network, were trained to determine local sample thickness from convergent beam diffraction (CBED) patterns of SrTiO3 collected in a scanning transmission electron microscope (STEM) at atomic column resolution. Acquisition of atomic resolution CBED patterns for this purpose requires careful balancing of CBED feature size in pixels, acquisition speed, and detector dynamic range. The training datasets were derived from multislice simulations, which must be convolved with incoherent source broadening. Sample thicknesses were also determined using quantitative high-angle annular dark-field (HAADF) STEM images acquired simultaneously. The regression CNN performed well on sample thinner than 35 nm, with 70% of the CNN results within 1 nm of HAADF thickness, and 1.0 nm overall root mean square error between the two measurements. The classification CNN was trained for a thicknesses up to 100 nm and yielded 66% of CNN results within one classification increment of 2 nm of HAADF thickness. Our approach depends on methods from computer vision including transfer learning and image augmentation.

Many-beam dynamical scattering simulations for scanning and transmission electron microscopy modalities for 2D and 3D quasicrystals

ABSTRACTWe present a general theory of electron scattering from both 2D and 3D quasicrystals, applicable to both transmission (forescatter) and scanning (backscatter) geometries. Specifically, simulations of conventional zone axis diffraction patterns, convergent beam diffraction patterns and electron backscatter diffraction for decagonal AlNiCo are presented. As expected, the geometry of the diffraction pattern is similar to kinematical patterns, but the intensity distributions show strong dynamical effects in all the modalities. Experimental electron backscatter diffraction patterns for AlNiCo are compared to simulated patterns for this 2D quasicrystalline structure as well as one of its crystalline monoclinic approximant phases, CoAl. While the simulated patterns from the quasicrystalline and approximant phases are very similar to the experimental patterns, direct comparison shows a better agreement with the decagonal phase.

On the role of the second-order derivative term in the calculation of convergent beam diffraction patterns

The simulation of (scanning) transmission electron microscopy images and diffraction patterns is most often performed using the forward-scattering approximation where the second-order derivative term in z is assumed to be small with respect to the first-order derivative term in the modified Schrödinger equation. This assumption is very good at high incident electron energies, but breaks down at low energies. In order to study the differences between first- and second-order methods, convergent beam electron diffraction patterns were simulated for silicon at the [111] zone-axis orientation at 20 keV and compared using electron intensity difference maps and integrated intensity profiles. The geometrical differences in the calculated diffraction patterns could be explained by an Ewald surface analysis. Furthermore, it was found that solutions based on the second-order derivative equation contained small amplitude oscillations that need to be resolved in order to ensure numerical integration stability. This required the use of very small integration steps resulting in significantly increased computation time compared to the first-order differential equation solution. Lastly, the efficiency of the numerical integration technique is discussed.

Using the TEM Condenser Lens to Switch between Image and Diffraction Modes

Central to the operation of the transmission electron microscope (TEM) (when used with crystalline samples) is the ability to go back and forth between an image and a diffraction pattern. Although it is quite simple to go from the image to a convergent-beam diffraction pattern or from an image to a selected-area diffraction pattern (and back), I have found it useful to be able to go between image and diffraction pattern even more quickly. In the method described, once the microscope is set up, it is possible to go from image to diffraction pattern and back by turning just one knob. This makes many operations on the microscope much more convenient. It should be made clear that, in this method, neither the image nor the diffraction pattern is “ideal” (details below), but both are good enough for many necessary procedures.

CBED electron beam drilling and closing of holes in decahedral silver nanoparticles

When a focused electron beam of 200keV energy with the characteristics used to obtain convergent beam diffraction patterns (CBED) in a transmission electron microscope (TEM) impinges on silver decahedral nanoparticles, a hole gets drilled in the site of incidence. The hole is the result of mechanisms of interaction which occur during the collision between the incident electrons and the target atoms, such as ballistic type, knock-on, temperature, etc. After the formation of the hole, and during observation time of the particle in the high resolution (HRTEM) mode, the hole is closed. The closing of the hole is an isostructural particle reconstruction, probably the result of the surface material diffusion together with the roughness at the atomic level of the hole's walls.

The phonon contribution to high-resolution electron microscope images

The amount of phonon scattering as a function of specimen thickness is determined for a clean silicon sample, free from amorphous surface layers, by measuring the diffuse scattering in energy-filtered convergent-beam diffraction patterns. It is found that for a 25 nm thick sample, only 7.5% of the intensity scattered to less than 18 nm −1 is phonon scattered. This means that in a typical high-resolution sample most of the diffuse scattering is caused by surface amorphous layers rather than phonon scattering.

Synthesis of BaAl2Si2O8from solid Ba–Al–Al2O3–SiO2precursors: Part III. The structure of BaAl2Si2O8formed by annealing at ≤650 °C and at 1650 °C

Analytical TEM and HREM have been used to examine the structure of BaAl2Si2O8crystals produced within oxidized Ba–Al–Al2O3–SiO2precursors upon annealing: (i) at ≤650 °C and (ii) up to 1650 °C. A BaAl2Si2O8polymorph with ac-axis parameter of 15.6 Å was detected after annealing at ≤650 °C. Stacking faults and antiphase boundaries were detected within this polymorph after the 650 °C treatment. After a 15 h heat treatment at 1650 °C, convergent beam diffraction patterns and HREM confirmed that the predominant phase wasβ–hexacelsian. Although antiphase boundaries were absent in theβ–hexacelsian crystals, dislocations and stacking faults were detected after the 1650 °C anneal. The generation of defects in BaAl2Si2O8crystals within specimens annealed at ≤650 °C and at 1650 °C is discussed in light of prior structural analyses.

Microstructural study of the Ni-doped 2212-phase of BiSrCaCuO superconductor single crystals

The microstructure of Bi 2Sr 2Ca 1Cu 2− x Ni x O y ( x=0.0, 0.02, 0.04) single crystals grown by the travelling solvent floating zone method have been investigated using transmission electron microscopy. High-resolution observations and diffraction patterns at the [100] zone axis show a very small change in the direction of the modulation wave with increasing of Ni concentration. Streak-shaped diffuse scattering along the row of modulation reflections was observed in all the specimens. Convergent beam diffraction patterns at the [001] zone axis showed two distinct symmetries: either a very strong asymmetry or a weak asymmetry in the b-plane. The strong asymmetry was attributed to the presence of intergrowth layers on the c-plane. The positions of Ni atoms within the structure of the crystal and their influence on the electric resistivity was discussed by considering the present experimental observation results.

Direct determination of phase from three-beam convergent-beam diffraction patterns of centrosymmetric crystals

Direct determination of phase from three-beam convergent-beam diffraction patterns of centrosymmetric crystals

The Symmetry of Three-Beam Scattering Equations: Inversion of Three-Beam Diffraction Patterns from Centrosymmetric Crystals

It is shown that for a centrosymmetric crystal, and within the range of validity of the three-beam approximation, the phases as well as the magnitudes of the three structure amplitudes can be measured uniquely and directly from the geometry of the intensity distributions in the discs of a convergent-beam diffraction pattern. In fact, the solution is given in terms of three distances measured on the diffraction pattern. It is further shown that the inversion is independent of thickness. Three proofs are given, each illustrating a different aspect of the physical processes involved. In the first, the fundamental symmetry of the diffraction process is shown to be that of the special unitary group of order three and the Gell-Mann representation is used to construct three sub-algebras, in terms of which the explicit solution is written. SU(3) is shown to have particular significance in crystallography, namely, that it is the group of lowest order with symmetries that can be analysed to yield structural phase. The second and longer method involves the projection of the scattering matrix into the spaces of the eigenvectors. Unlike the first method, this makes use of a basis; however, it is not necessary to calculate explicitly either the eigenvectors or the eigenvalues. The third method, based on the Bloch-wave expansion, shows that the system is characterized by three lines, which are ruled on one of the dispersion surfaces, and that all of the information in the system is embodied in these lines. Although this theory is scalar and developed here for electron diffraction, it can apply equally to the right circular component of the wave function of X-rays. Some brief remarks are made on the practicability of this method based on preliminary experiments that indicate that phase is the easiest of the parameters to measure.

Measurement of TEM primary energy with an electron energy-loss spectrometer

We describe a simple technique for measuring the primary energy of a transmission electron microscope (TEM) using an electron energy-loss spectrometer. The technique is checked against a measurement based on simulating a convergent beam diffraction pattern, and found to be accurate to better than 0.1%.

Inversion of convergent-beam electron diffraction patterns

The problem of recovering the structure factors that contribute to a zone-axis convergent-beam diffraction pattern is discussed. It is shown that an automated matching procedure that minimizes the sum-of-squares difference between experimental and simulated patterns is effective whether one is refining accurate structure factors in a known crystal or attempting ab initio structure determination. The details of the minimization method are analysed and it is shown that a quasi-Newton method that uses analytically derived gradients is particularly effective when several structure factors are varied. The inversion method for ab initio structure determination is tested on the [110] axis of GaP, using simulated patterns as ideal 'experimental' data.

Quantitative absorption corrections for electron diffraction: Correlation between theory and experiment

The absorptive potential due to thermal diffuse scattering (TDS) of fast electrons is calculated using an Einstein model. The TDS potential is substantially different from the elastic potential, being extremely peaked on atomic positions with virtually no absorption in the channels between atomic planes. This absorptive potential is used to determine imaginary (absorptive) components of the eigenvalues for each branch of the dispersion surface, using a Bloch wave description for propagating the fast electron wavefunction through a crystal. Large-angle convergent-beam electron diffraction (LACBED) contrast is calculated and compared with experiment using a 300 keV beam for various zone axes of silicon, GaAs and spinel. Changes in mean free paths for TDS under strong dynamical diffraction conditions as a function of crystal orientation are calculated, showing strong channelling/blocking characteristics due to the extremely localized TDS potential. The usual model for taking dynamical absorption effects into account, i.e. scaling the absorptive potential to the elastic potential, has severe limitations and fails to quantitatively predict LACBED contrast. We demonstrate that the Einstein model provides quantitative agreement with experiment, without the use of fitted parameters. Theory is also correlated with convergent-beam diffraction patterns, where rockin-curve contrast is used to determine the polarity of a multiply twinned epilayer of CdTe. This model is also applied to the thickness fringe method for determining the composition of AlGaAs quantum wells. Thickness fringe calculations using exact matrix methods for determining complex eigenvalues are compared with perturbative methodes.

Ultrathin silicon membrane thickness determination by CBED and measurement of plasmon mean free path

The lower limit of accurate thickness measurement using two beam CBED patterns is usually about one extinction distance for the reflection used. We have used (111) symmetric CBED patterns to measure thin silicon membrane thicknesses as low as 130 Å by comparing experimental patterns with computer simulated CBED patterns. The silicon plasmon mean free path was also measured using these thickness values.Symmetric convergent beam diffraction patterns of (111) silicon in the thickness range of 130 Å to 1300 Å were obtained in a VG HB501A STEM with a 5 Å probe (8 mrad convergence angle) scanning a 100 Å × 100 Å area. The sample was made by ion implantation, anodic etching and annealing. Subsequent photolithography and reactive ion etching thinned the specimen down further to as thin as 100 Å. The sample was chemically cleaned by the Shiraki method before being loaded into the microscope.

On the use of convergent-beam electron diffraction for identification of antiphase boundaries in GaAs grown on Si

Dynamical coupling effects between the (200) reflection and weak odd-index reflections in the Bragg position in convergent-beam diffraction patterns has been used to detect antiphase boundaries (APBs) in GaAs grown on (001) Si. It was shown that APBs lie in most cases on energetically favorable {110} planes and effectively stop the propagation of dislocations, twins and stacking faults. The formation of APBs is promoted by Si surface contamination and irregularities.

Improving the accuracy of convergent-beam thickness measurements

Convergent-beam diffraction patterns taken at appropriate “two-beam” conditions allow simple, rapid determinations of a specimen's thickness, extinction length and even its anomalous absorption coefficient (1,2). We here note three points to consider when obtaining the pattern.First, in thickness measurements the ratio of the fringe spacing to the spacing between the disks is utilized; there is an underlying assumption that the two distances are on the same angular scale. This assumption is incorrect if the illumination crossover is not in the plane of the specimen and simultaneously, the diffraction lens is focused incorrectly. If the crossover is at the specimen (Fig. 1a), varying the focus of the diffraction lens (changing w) varies the distance between the disks and the sizes of features within the disks in the same way, only the magnification of the pattern is changed. Likewise, if the diffraction lens is focused correctly, on the back focal plane of the objective lens, the angular scale within the disks matches that between the disks and neither scale is affected by variations in the illumination.