Large-angle Convergent-beam Electron Diffraction Patterns Research Articles

Machine learning calculation of large-angle convergent-beam electron diffraction patterns

Machine learning calculation of large-angle convergent-beam electron diffraction patterns

Evaluation of accuracy in the determination of crystal structure factors using large-angle convergent-beam electron diffraction patterns.

The accuracy of electron density distribution analysis using large-angle convergent-beam electron diffraction (LACBED) patterns is evaluated for different convergence angles. An orbital ordered state of FeCr2O4 is used as an example of the analysis. Ideal orbital-ordered and non-ordered states are simulated by using orbital scattering factors. LACBED patterns calculated for the orbital-ordered state were used as hypothetical experimental data sets. Electron density distribution of the Fe 3d orbitals has been successfully reconstructed with a higher accuracy from LACBED patterns with convergence angles larger than 15.2 mrad, which is 4 times as large as that for conventional convergent-beam electron diffraction patterns. Excitation of particular Bloch waves with the aid of LACBED patterns has a key role in the accurate analysis of electron density distributions.

New developments in the characterization of dislocation loops from LACBED patterns

The characterization of the Burgers vector of dislocations from large-angle convergent-beam electron diffraction (LACBED) patterns is now a well-established method. The method has already been applied to relatively large and isolated dislocation loops in semiconductors. Nevertheless, some severe experimental difficulties are encountered with small dislocation loops. By using a 2 microm selected-area aperture and a carbon contamination point to mark the loop of interest, we were able to characterize both the plane and the Burgers vector of dislocation loops of a few tens of nanometres in size present in Al-Cu-Mg alloys.

Effect of anisotropic temperature factors on convergent-beam electron diffraction intensities and measurement of the local change in the oxygen concentration of YBa2Cu3O y

The local oxygen concentration of the high-T c superconductor YBa2Cu3O y was measured from large-angle convergent-beam electron diffraction patterns using a transmission electron microscope equipped with a field emission gun with an in-column-type energy filter. The anisotropic effect of thermal vibrations of atoms was considered in the analysis of the oxygen concentration, based on the many-beam dynamic theory. The observed fluctuation in the oxygen concentration can explain the peak effect in the J c–H curve, the critical current density J c plotted as a function of applied magnetic field H.

CBED and LACBED: characterization of antiphase boundaries

Convergent-beam electron diffraction (CBED) and large-angle convergent-beam electron diffraction (LACBED) techniques are well adapted to the characterization of several types of crystal defects. In fact, dislocations, grain boundaries and stacking faults have already been successfully characterized with these methods. In the present paper, we describe the CBED and LACBED characterization of another type of crystal defect showing a special interest in materials science: antiphase boundaries (APBs). The first part of the paper is devoted to the determination of the effects of antiphase boundaries on CBED and LACBED patterns that could be expected from a theoretical point of view. It indicates that the superlattice excess lines present on these patterns are split into two lines with equal intensity when the incident beam is located on an APB. In the second part, we experimentally test these theoretical predictions on a specimen showing two different known types of antiphase boundaries. In a third part we indicate how these methods could be used to identify unknown APBs in a specimen. Finally, the advantages and disadvantages of both methods for the characterization of antiphase boundaries are discussed.

Stress fields near interfaces of aluminium-based metal-matrix composites

Abstract Large-angle convergent-beam electron diffraction (LACBED) is used to investigate the interfacial strain fields in a short-fibre-reinforced Al-based metal-matrix composite. LACBED patterns are simulated using the dynamic scattering theory with local variations in the scattering vectors caused by lattice distortions. Comparison of experimental and simulated patterns permits local strains to be estimated. Thermal strains and surface relaxation of the thin foil for transmission electron microscopy are considered. Long-range thermal strains caused by the fibre overlapping with localized high strains produced by spinel grains at the fibre boundary are analysed. In Al grains, local stress concentrations are reduced by the emission of dislocations. In Si precipitates, high stresses at the Si-fibre interfaces are maintained. Short-range stresses from inhomogeneities at the Si-fibre interfaces and not the long-range thermal stresses from the whole fibres dominate in Si precipitates.

Stress fields near interfaces of aluminium-based metal-matrix composites

Abstract Large-angle convergent-beam electron diffraction (LACBED) is used to investigate the interfacial strain fields in a short-fibre-reinforced Al-based metal-matrix composite. LACBED patterns are simulated using the dynamic scattering theory with local variations in the scattering vectors caused by lattice distortions. Comparison of experimental and simulated patterns permits local strains to be estimated. Thermal strains and surface relaxation of the thin foil for transmission electron microscopy are considered. Long-range thermal strains caused by the fibre overlapping with localized high strains produced by spinel grains at the fibre boundary are analysed. In Al grains, local stress concentrations are reduced by the emission of dislocations. In Si precipitates, high stresses at the Si-fibre interfaces are maintained. Short-range stresses from inhomogeneities at the Si-fibre interfaces and not the long-range thermal stresses from the whole fibres dominate in Si precipitates.

Higher‐order Laue zone line contrast in large‐angle convergent‐beam electron diffraction around a dislocation

The physical picture of higher-order Laue zone (HOLZ) line contrast in a large-angle convergent-beam electron diffraction pattern around a dislocation, which is used for determining the Burgers vector, was examined. To evaluate the analytical expression of diffracted wave amplitude, we introduced an approximate form of the atomic displacement field of a dislocation. We showed that the four features of the HOLZ line contrast, that is, splitting, fading, bending and periodical contrast can be explained by analysis of the atomic displacement field. The localized lattice plane bending around a dislocation core made a HOLZ line split, fade and bend. However, we found that the periodical contrast of a HOLZ line was produced by the change of phase difference of the atomic displacement field between the crystals above and below the slip plane across the dislocation line.

Large angle convergent beam electron diffraction strain measurements in high dose helium implanted silicon

Large angle convergent beam electron diffraction (LACBED) technique has been applied to <110> TEM cross section of silicon samples implanted with 2×1016 cm−2 He ions at an energy of 20 KeV in order to evaluate the stress/strain field in the implanted layer. The stress/strain field depends on the mismatch between the lattice of the silicon substrate and the one of the defective layer which contains clusters of point defects and small He bubbles. Lattice mismatch causes changes in the spacing and inclination of diffraction planes producing a shift and a rotation of diffraction intensity lines (Bragg contours (BC)) visible in LACBED patterns. In particular, when the electron beam is parallel to the rotation axis, the BC simply rotate. This is the case of mismatches observed with (333) BC when the electron beam is incident on the sample along a direction close to <110> zone axis. Measurements show a peak of the stress/strain field (intensity 1.5 GPa) at a depth close to the helium projected range, where small bubbles occasionally form aggregate oriented along <011> direction.

Application of the large angle convergent beam electron diffraction technique to the characterisation of martensitic phases in Cu–Zn–Al alloys

Martensitic phases in Cu–Zn–Al alloys have close packed structures which can be described as a face centred tetragonal (fct) lattice into which stacking faults are periodically inserted every second or third close packed plane. The tetragonality c / a of the fct cell is an important parameter which is related to the martensitic transformation temperature to the parent B2 or L2 1 phase. When diffusion is allowed in the martensitic phases, a process of stabilisation takes place. This process results in an increase of the transformation temperature to the parent phase and involves changes in the tetragonality of the fct cell. In order to study the tetragonality of the martensitic phases in Cu–Zn–Al alloys, the large-angle convergent beam electron diffraction (LACBED) technique is used. Different LACBED patterns are obtained to find an adequate orientation for the determination of the tetragonality, and its evolution during stabilisation. The results are compared with X-ray measurements available in the literature. The accuracy of the method and its applicability to the study of stabilisation processes are discussed.

Accurate measurement of grain boundary misorientation by Large Angle Convergent Beam Electron Diffraction

A new method using Large Angle Convergent Beam Electron Diffraction (LACBED) patterns is proposed to measure accurately the grain boundary misorientation. The LACBED patterns which are obtained with a defocused convergent electron beam having a convergence semi-angle in the range 1 to 5o contain very sharp deficiency lines. Due to the good quality of the LACBED patterns, these sharp deficiency lines can be used to measure with great accuracy the grain boundary misorientation. In addition, since the LACBED method is a defocus mode method, the patterns contain at the same time information on the reciprocal space (the deficiency lines typical of the crystal orientation of the two grains on each side of the grain boundary) and on the real space (the image of the grain boundary). We describe a method which allows the identification of the misorientation from these LACBED patterns. The main point to consider is the accuracy which is about 0.05o. It is much better than the one obtained from other conventional methods used to measure this misorientation.

Determination of the orientation of a stacking fault by large-angle convergent-beam electron diffraction (LACBED)

The asymmetrical bending of the stacking fault fringes in the dark-field large angle convergent beam electron diffraction patterns is reported and utilized to determine the sense of the stacking fault. A stacking fault pyramid in GaAs is studied by analysing the enteraction between the stacking fault and the diffraction lines in the LACBED patterns so as to determine the intrinsic/extrinsic stacking faults and the displacement vector R.

Large-angle convergent-beam electron-diffraction study of coherent precipitates and decorated dislocations

Conventional methods of convergent beam electron diffraction (CBED) use a fully converged probe focused on the specimen in the object plane resulting in the formation of a CBED pattern in the diffraction plane. Large angle CBED (LACBED) uses a converged but defocused probe resulting in the formation of ‘shadow images’ of the illuminated sample area in the diffraction plane. Hence, low-spatial resolution image information and high-angular resolution diffraction information are superimposed in LACBED patterns which enables the simultaneous observation of crystal defects and their effect on the diffraction pattern. In recent years LACBED has been used successfully for the investigation of a variety of crystal defects, such as stacking faults, interfaces and dislocations. In this paper the contrast from coherent precipitates and decorated dislocations in LACBED patterns has been investigated. Computer simulated LACBED contrast from decorated dislocations and coherent precipitates is compared with experimental observations.

Effects of elastic relaxation on large-angle convergent-beam electron diffraction from cross-sectional specimens of GexSi1−x/Si strained-layer superlattices

Abstract A large-angle convergent-beam electron diffraction pattern with fine diffraction lines from a cross-sectional specimen of Gexsi1−x/Si strained-layer superlattices can give much information on local strain and misfit stress relaxation. The diffraction lines in the GeSi layers are shifted from those in the Si layers by the misfit strain and the strain relaxation. In this paper we shall demonstrate that the effects of elastic relaxation and the residual strains can be separated.

Surface relaxation of strained heterostructures revealed by Bragg line splitting in LACBED patterns

Bragg line splitting near the shadow image of a thin strained InGaAs layer, buried in GaAs and without strain relief by misfit dislocations, was found in large angle convergent beam electron diffraction (LACBED) patterns of cross-section specimens. The surface relaxation of the built-in strain and the Bragg line intensities were calculated. A qualitative agreement between the experimental Bragg line splitting and the theoretical calculations is demonstrated Closer matching was achieved using a “line-force” model of the surface relaxation, whereas a Fourier transform solution showed significant underestimation of the Bragg line splitting. The possibility of characterising the built-in strain in thin strained layers, by measuring this Bragg line splitting in LACBED patterns, has been explored.

Convergent-beam electron diffraction studies of epitaxial Si/SiO2systems

Abstract Convergent-beam electron diffraction (CBED) techniques have been applied to the study of silicon layers grown laterally on partially oxidized silicon wafers by liquid-phase epitaxy. Energy filtering of the electrons in the microscope provides CBED patterns from cross-sectional and plan-view specimens of large thickness with improved contrast and angular resolution. Cross-sections from the interfacial regions show a splitting or a broadening of the rocking profile of lines in CBED patterns. Strains at the Si–SiO2 interfaces are deduced from the patterns and related to relaxation effects in the special geometry of the cross-sectional specimens. Inference to bulk systems reveals that the Si lattice is in a state of tetragonal distortion close to the Si/SiO2 interface. Large-angle CBED patterns from plan-view specimens reveal a bending of Si layers relative to the substrate. Examples in the study of lateral coalescence of Si layers are demonstrated, such as the reversal of bending of the layers at th...

Reasonably good images of dislocations in LACBED patterns and effects of dislocation strain fields on the Bragg lines

An improved large-angle convergent beam electron diffraction (LACBED) experiment method using a Philips CM12 electron microscope is discussed. Dislocations in silicon parallel to the Bragg lines have been studied by this improved LACBED technique. Images of dislocations of reasonably good spatial resolution superimposed on LACBED patterns have been obtained. It has been found that only when the image of the dislocation is parallel and close to the low-order contour with g · b ≠ 0 can it be formed with reasonably good contrast in the LACBED patterns. Both the image of the dislocation and the changes of the contours can be visible in a single LACBED pattern, making it a convenient technique for studying the strain field of a dislocation.

Burgers vector determination of decorated dislocations in γ-TiAl by diffraction contrast and large-angle convergent-beam electron diffraction

Abstract Decorated and undecorated dislocations in γ-TiAl have been studied by conventional transmission electron microscopy using diffraction contrast and by large-angle convergent-beam electron diffraction (LACBED). The results of the Burgers vector determination for undecorated and decorated dislocations using the different techniques have been compared. For the decorated dislocations the contrast from the decorating particles and the underlying dislocation have been separated and the misfit introduced by the precipitates has been determined. Computer simulations of the contrast from decorated dislocations in LACBED patterns have been performed. The rules governing the dislocation contrast in LACBED patterns have been discussed and extended to the case of decorated dislocations. A new fringe-counting rule to determine the Burgers vectors of dislocations decorated by misfitting precipitates has been proposed. Remarkably good agreement of the computer-simulated LACBED contrast with experimental observations has been achieved.

Structure of a metastable Al-Ge phase determined from large angle CBED patterns

Abstract The structure of a new metastable Al-Ge phase recrystallized at 300°C from amorphous films with equiatomic composition deposited on to NaCl substrates cooled with liquid nitrogen was determined by convergent beam electron diffraction (CBED). The micron-sized crystals were tetragonal with space group 14/mcm, lattice parameters a = 6.13 Å and c = 4.92 Å, and composition Al0·9 Ge0·9. The structure was the C16 type with nominal AB 2 composition, although there was no evidence for preferential location of Ge on either A or B sites. The A atoms occupied 4(a) sites, and the B atoms were located on 8(h) sites with x = 0·158. Conditional Patterson transforms parallel to the c axis were calculated from kinematic intensities measured in focused large-angle CBED patterns. The contour maps showed clear peaks from A-B and B-B interatomic vectors. Dynamical perturbations reduced peak visibility but did not affect peak positions. The x parameter for B atoms was refined from the quasi-kinematic intensities of first-order Laue zone reflections diffracted from Bloch states localized on B atom strings in conventional CBED patterns.

High spatial resolutions of diffraction information in large-angle convergent-beam electron diffraction patterns from cross-sectional specimens of GexSi1-x/Si strained-layer superlattices

High spatial resolutions of diffraction information in large-angle convergent-beam electron diffraction patterns from cross-sectional specimens of Ge_<i>x</i>Si_1-<i>x</i>/Si strained-layer superlattices