Convergent-beam Diffraction Patterns Research Articles

Structure information from wide-angle convergent-beam diffraction patterns

Structure information from wide-angle convergent-beam diffraction patterns

On the atomic structure of the Pd2Si/(111)Si interface

Abstract The structure of the epitaxial Pd2Si/(111)Si interface has been investigated by transmission electron microscopy (TEM). Lattice imaging and conventional TEM on plan-view specimens show that the Pd2Si grains are often misoriented, by typically 4° → 7°, from the epitaxial relation of (0001)Pd2Si//(111)Si, [1010]Pd2Si//[011]Si. Quantitative texture measurements made by taking convergent-beam diffraction patterns from areas containing individual Pd2Si grains show that misorientations are mostly described by tilting about <110> directions in the film plane. Lattice imaging in (100) cross-sectional samples reveals more clearly the nature of the Pd2Si/(111)Si interface and also shows that individual Pd2Si grains may be considerably bent. The origin of the grain misorientations and their significance in understanding the atomic structure of the Pd2Si/(111)Si interface is discussed.

The analysis and application of dynamical effects in holz patterns

The dynamical effects associated with crossovers of deficit lines in the central disc of convergent-beam diffraction patterns are analysed. It is demonstrated that suprisingly accurate predictions of these effects can be obtained analytically for a symmetric pattern, using a simple three-beam approximation. The physical insight thus gained into the problem is discussed and applied in the context of chemical analysis.

Kossel diagrams show electric-field-induced cubic-tetragonal structural transition in frustrated liquid-crystal blue phases.

Convergent beam diffraction patterns from a bcc blue-phase (I) monocrystal in an electric field applied in the [110] direction show this twofold axis transforming through an orthorhombic distortion to become, at a critical field, the fourfold axis of a tetragonal crystal. The implication on structures of blue phase I is important. Although the transition is weakly first order because the two order parameters describing it are coupled, the diffraction pattern changes continuously through the transition.

Electron diffraction from modulated structures. II. Application to the ternary modulated phase NiGeP

For pt.I see ibid., vol.19, p.3497 (1986). The extraction of quantitative information from large angle, satellite dark field, convergent beam diffraction patterns taken from the incommensurately modulated ternary phase NiGeP is described. Expressions for the incommensurate satellite structure factors are derived in terms of an initially unconstrained phonon eigenvector. The little-co-group of the modulation wave-vector is used to derive the normal modes of the unmodulated lattice and the appropriate eigenvectors for two of the modulations observed in experiment. By fitting the variation of satellite diffraction intensity with incident orientation to that observed experimentally, the eigenvector components of one of these are determined.

Determination of the anisotropy of surface free energy of fine metal particles

Relative values of the anisotropic surface free energy of several metallic powders have been obtained by examining the crystallography of ultrafine particles ( < 100 nm in size). The material is produced by direct condensation of vapours in an inert gas plasma reactor. Crystallographic characterization of individual powders was accomplished using convergent beam diffraction patterns (CBDP). Accurate analysis utilized the intense Kikuchi lines in the CBDP. The majority of the particles had assumed their equilibrium-facetted morphologies as predicted by the Wulff construction. In this paper, the morphology of the powder particles and their crystallographic characterization will be described. The results for the relative surface free energies of the facets will be presented and compared to theoretical calculations in literature.

Electron diffraction phenomena observed with a high resolution STEM instrument

AbstractBecause of the high brightness of the cold field emission source used in a dedicated scanning transmission electron microscopy (STEM) instrument, it is possible to focus electrons to a cross‐over of width 3Å or less and, with a suitable detection system, to obtain diffraction patterns from specimen regions of this size or greater. Coherent interference effects are visible in shadow images (in‐line holograms) and in convergent beam diffraction patterns. Special techniques have been developed for gathering information from the diffraction patterns for application to the study of the structures of crystal defects, crystal surfaces and small particles. Possibilities have been explored for holographic reconstruction from shadow images.

Recent applications of STEM to small particles

It is nowadays routine to use STEM to identify particles of order 1 nm in diameter. Such particles often occur in semiconductor materials, minerals and metals, and of course in supported catalysts. An important application is to aerosols and smokes, where high resolution STEM should permit identification and classification of particles hitherto analysed only by wet chemistry. A simple collector is described which can be used together with classical methods. In the dedicated STEM, it has so far proved difficult to acquire high-quality large-angle convergent-beam diffraction patterns. A new technique of direct photography in the UHV environment gives efficient parallel recordings of such patterns, and permits very rapid acquisition of information from nanometer particles.

Comparison of convergent-beam electron diffraction methods for determination of foil thickness

Abstract The methods of determining foil thickness from convergent-beam diffraction patterns, the Kelly method and the Ackermann method, have been compared in experiments using silicon and iron foils. It was necessary to use the Kelly method to determine the effective extinction distances experimentally. However, tests showed that the thickness determined by the Ackermann method is less sensitive to both systematic and random variations in the data, particularly to variations in the value of the first intensity maxima, for which the percentage errors are largest. The precision in thickness measurement achieved in the study was of the order of 5%. The deviation in thickness determinations by both methods was less than 2%. The two methods are roughly equivalent unless errors can be reduced below this level.

Measurement of foil thickness and extinction distance by convergent beam transmission electron microscopy

Abstract The procedures previously recommended for the determination of foil thickness from convergent beam diffraction patterns are shown to suffer from considerable ambiguity. Two-beam dynamical calculations have been made with ALLOWANCE for the effects of absorption. The computed intensity profiles are shown to match experimentally observed profiles closely and to provide an unambiguous means of determining the correct foil thickness and extinction distance to accuracies of ± 5% or better. The observed extinction distances for pure copper are less than published theoretical values because of the effects of systematic reflections, which cannot be entirely avoided in practice. Extinction distances have also been determined for aluminium, for Al-l%Mg-l%Mn and for type 304 stainless steel.

Mirror-symmetric and non-mirror-symmetric glide planes in CuAsSe 1−xS x: I. A convergent beam electron diffraction study

The question of a breakdown of Friedel's law occuring in electron diffraction from parallel-plate crystals purely due to the symmetry-breaking effect of translation glide-plane vectors has recently been the source of some debate in the literature. Convergent beam diffraction patterns from cleavage crystals of the compounds CuAsSe 0.8S 0.2 and CuAsSe, having the space group Pbna, are used to illustrate the point that the symmetry-breaking effect described is amplified in certain crystals settings close to the principal zone and can be used to distinguish b- and n-glides in orthorhombic structures in a practical way. Calculations show a similar effect at the exact zone setting which, however, would be less accessible experimentally. These results lend support to the long-held belief that CBED pattern symmetries are the transformed symmetries of a parallel-sided crystal slab, in accordance with standard N-beam transmission theory, and that this result is of positive value in space group and structure determination.

Error bars in CBED symmetry?

Convergent-beam electron diffraction (CBED) is a powerful tool in analytical electron microscopy. Analysis of the patterns may reveal the crystal structure of the specimen. However, if the crystal is not perfect in the region probed by the electron beam, patterns can be degraded and the analysis may be ambiguous. Convergent-beam diffraction patterns are never perfect, yet there has been little discussion, to date, of how far from a perfect symmetry a convergent-beam pattern may be and still be assigned that symmetry. The human eye is acutely sensitive to pattern recognition and it is often easy to spot small deviations from perfect symmetry. The question is, given a pattern that one knows is from a near-perfect crystal, how far can the symmetry deviate from perfection before one must say that a lower symmetry is observed? The aim of this work was to carefully analyze CBED patterns from a number of known materials and observe to what degree the pattern symmetries deviated from perfection. Analysis was carried out both manually and with the aid of a computer. An attempt has been made to establish confidence limits for use in CBED pattern analysis.

A retabulation of the 80 layer groups for electron diffraction usage

The 80 space groups of infinitely extended layers are identified as the defining groups for transmission electron diffraction symmetries obtained from lamellar crystals. These layer groups are retabulated using a notation which characterizes the symmetries of convergent-beam diffraction patterns. The new tabulation provides a means for determining the three-dimensional space group of a particular structure from one or more convergent-beam zone-axis patterns. This is a two-stage process, involving determination of a layer-group corresponding to a principal zone-axis pattern, followed by identification, where necessary, of the appropriate class-equivalent subgroup. For this final identification, the three-dimensional extinction conditions, determined from an alternative set of convergent-beam zone-axis patterns, are required. In terms of standard group symbols [e.g. Vainshtein (1981). Modern Crystallography I. Berlin: Springer], the one-way interrelation between patterns and space groups G32 → G33 (space group analysis) is given. The inverse problem, equally accessible from group theory, of providing the interrelation G33 → G32 (pattern symmetry prediction) is left for separate tabulation.

An introduction to the STEM

It is particularly appropriate for this Journal to devote one of its issues to the subject of the scanning transmission electron microscope (STEM) and its uses because the initial stimulus for its invention was precisely the problem of discerning ultrastructural details in biological material. To a large extent the capabilities of the instrument have been shown to offer the potential of solving many such problems and what is most needed today is to put such instruments in the hands of biologists together with the information on how and when to use them. This issue should go a long way in satisfying this latter need. The purpose of this article is to try to provide a setting for the more detailed expositions which follow. In order to do this we must necessarily give a very general treatment and avoid detail. In addition, we will concentrate on those aspects of the STEM which apply to biological uses, and we will therefore ignore the more esoteric applications, such as convergent beam diffraction patterns.

Foil thickness measurements from convergent-beam diffraction patterns An experimental assessment of errors

Abstract Foil thickness measurements from convergent-beam electron diffraction (CBED) patterns may be easily made using a technique based on the two-beam approximation to dynamical diffraction theory. A previous theoretical study showed that, under certain conditions, multiple-beam interactions could seriously affect the accuracy of the technique by causing systematic errors. In the present study, the precision of a CBED technique for the measurement of foil thickness was studied experimentally by analysing diffraction patterns taken at several locations using four different diffraction vectors in a Co-based alloy. A precision of ∼3% was achieved when measurements from a single location taken under different conditions were compared. For the individual thickness measurements, using patterns from 220 or 311 reflections, the width of the 95% confidence intervals was in no instance greater than 4% of the measured thickness. Values of ξg, which are also obtained from the CBED analysis, showed a 95% confidence...

High-resolution images of bent crystals having rutile-type structures: Tin dioxide

Abstract High-resolution images of SnO2, crystals, oriented into the [001] zone, show 4·7 × 4·7 A2 detail produced by 100 and 010 reflections. Similar images are obtained at both 200 and 500 kV. Since these reflections are both kinematically and dynamically forbidden, for symmetrical zone orientations, the image contrast is not predicted using usually-acceptable computer-simulation techniques. On the other hand convergent-beam diffraction patterns are quite consistent with the expectations of dynamical scattering theory, assuming the accepted structure and space group. It is suggested that the apparently anomalous behaviour of the images is due to breakdown in symmetry caused by elastic bending, when the screw-axis operations, responsible for extinction of 100 and 010, will be lost. Image calculations for a simple bent crystal show that radii of curvature of 10–20 μm, extending over lateral extent 50–100 A, are more than sufficient to destroy the screw operations effectively as far as dynamical scattering...

A simple method for the determination of structure-factor phase relationships and crystal polarity using electron diffraction

Multiple electron scattering between weak beams has been used as the basis for a simple method to determine the absolute polarity of some non-centrosymmetric crystals. For crystals with the sphalerite structure many orientations have been found in which small departures from centrosymmetry produce large effects on the convergent-beam diffraction patterns (microdiffraction). The effects are reasonably independent of thickness and so can be analyzed qualitatively without the use of computers.

The application of convergent-beam electron diffraction to the detection of small symmetry changes accompanying phase transformations I. General and methods

Abstract This paper considers the origins of convergent-beam diffraction patterns (CBDPs) and the particular uses of high-order Laue zone (holz) lines which are a feature of these patterns. Small changes in the arrangement of the holz lines, corresponding to changes in the lattice parameter and symmetry of the crystal giving rise to them, are discussed, and a technique for their simulation described. The advantages and limitations of the convergent-beam diffraction technique are considered.

Foil thickness measurements from convergent-beam diffraction patterns

Abstract The analysis of convergent-beam electron diffraction patterns for foil thickness is easily carried out in the two-beam approximation to dynamical diffraction theory. The effects of this approximation on the accuracy of foil thickness determinations are considered, as well as the range of thicknesses which can be measured with the technique. Inaccuracies due to multiple-beam effects are minimized by avoiding diffracting conditions involving low-order reflections. For 100 keV electron energy, errors of less than 2% in thickness determination are possible in Al, Cu and Au, if the diffraction vector g is equal to or larger than 200, 220 or 311 respectively. The minimum thickness measurable for these materials diminishes as |g| increases, but is approximately 20 nm for the lower-order reflections. The maximum thickness measurable is limited by absorption, and is estimated for Al, Cu and Au to be approximately 600, 130 and 40 nm respectively.

Coherent interference effects in SIEM and CBED

The coherent convergent incident beam produced by the field emission gun of a STEM instrument allows the observation of a number of unusual interference effects in the shadow images (SIEM) and convergent beam diffraction (CBED) patterns visible on the detector plane. Shadow images of thin crystals display the electron Ronchigrams having a form sensitive to the defocus and aberrations of the objective lens. For large crystal lattice spacings the Ronchigrams show characteristic ellipses of low contrast. CBED patterns of thin crystals show symmetries and intensities which vary with the position of the incident beam within the unit cell. Discontinuities in the specimen such as the edges of crystals show striking Fresnel diffraction effects in SIEM. In CBED patterns they give rise to the splitting of diffraction spots. If the incident beam is parallel to a smooth face of a small crystal the potential field outside the crystal gives rise to strong refraction effects.