Higher-order Laue Zone Research Articles

Higher order Laue zone patterns in convergent beam electron diffraction and determinations of local lattice parameters in .ALPHA.- and .ALPHA.2-phases of a Cu-20at%Al alloy.

In order to clarify the applicability of higher order Laue zone (HOLZ) patterns in convergent beam electron diffraction to the determinations of local lattice distortions in two-phase alloys, we discussed experimental conditions affecting the accuracy, and observed HOLZ patterns of a Cu-20at%Al alloy, in which small particles of α2-phase with one dimensional long period superstructure are precipitated in the matrix of fcc α-phase. It was shown that the accuracy is affected by specimen thickness as well as beam direction, and that lattice parameters along the [100] and [010] axes can be determined from a [114] HOLZ patterm with an error less than one part in a thousand. The [114] HOLZ patterns were obtained both from small regions in α-matrix and α2-particles. Slight changes in lattice parameters were detected as a function of position with a high spatial resolution.

Electron Channeling Analysis of Elastic Strains in InGaAs Thin Films

AbstractInx Ga1-x As thin films were grown by MBE on (001) GaAs substrates. The associated 1% lattice mismatch resulted in the development of an elastic strain field in the systems. Electron channeling patterns (ECP) were then obtained from these samples in an SEM at different accelerating voltages, allowing data to be obtained over various information depths within the samples while keeping them intact. The ECPs showed sensitivity to the elastic strains both parallel and perpendicular to the film/substrate interface. Certain high order Laue zone (HOLZ) line positions showed good sensitivity to the Poisson strain in the films due to a rotation of atomic planes. These line positions varied with film thickness and distance from the interface. The technique shows promise as a tool for relatively easy elastic strain determination. Its limitations will also be discussed.

Microdiffraction from Cleaved Si-Si1-xGex Multilayers

AbstractUsing the nanometer probe available in the dedicated scanning transmission electron microscope (STEM) local structural information can be obtained from individual layers in [100] grown Si-Si1-xGex multilayer structures. Furthermore the small probe size enables cleaved specimens with their very large wedge angles to be analyzed in cross-section. Diffraction patterns are shown from multilayers of varying periodicity. Analysis of the patterns concentrates on the higher order Laue zone (holz) reflections in the high angle excess ring . The behaviour of the excess holz reflections indicates the transition from a strained layer superiattice to a dislocated structure as the thickness of the layers increases for a given composition.

The simulation of HOLZ line positions in electron diffraction patterns: a first order dynamical correction

The accuracy of the geometric model for the simulation of higher order Laue zone (HOLZ) line positions in electron diffraction patterns is discussed and a modification proposed in which a first order correction is made for the position of the first branch of the zero layer dispersion surface. The modification provides a physically more realistic picture of the scattering process, and the situations in which the neglect of these dynamical effects might lead to significant errors are assessed. The degree to which it is worthwhile to include the effects of increasing numbers of diffracted beams is also considered.

Convergent-beam imaging—a transmission electron microscopy technique for investigating small localized distortions in crystals

Abstract A new transmission electron microscopy technique is described, convergent-beam imaging (CBIM), in which an image is formed using a convergent beam focused above or below a thin crystalline specimen. Superimposed on the image are higher-order Laue zone (HOLZ) lines, the displacements of which map the spatial variation of strains, lattice parameters and crystallographic rotations. The image has its normal resolution, the superimposed diffraction information has an angular resolution of about 10−4 rad, and this diffraction information comes from regions of the specimen defined approximately by the cross-over size of the electron probe size, broadened by beam spreading. The visibility of HOLZ lines in the CBIM image is significantly improved by cooling the specimen. The CBIM technique is illustrated by its application to a Si/GexSi1−x strained-layer structure, where spatial changes in the lattice parameter and crystal symmetry are revealed by the relative positions of the HOLZ lines in the Si and all...

Measurement of small elastic strains in silicon using electron channeling patterns

A silicon single-crystal slab 0.15 mm in thickness was bent to produce small, nonuniform surface strains of the order of 0.2%. The electron channeling patterns were observed in a JSM 840 SEM (scanning electron microscope) at an accelerating voltage close to 25 kV. Proper choice of the triangles formed by intersecting channeling lines of zero-order and of higher-order Laue zones allows one to measure the changes in their dimensions caused by imposed strain. It was estimated that the lower limit of detectable elastic strain is close to 0.1%. The possibilities of using this method for estimation of the average elastic strains in thin epitaxial layers are discussed.

Electron Diffraction Study of α- and α T -AlFeSi

Electron diffraction patterns from a-AIFeSi and αT-AlFeSi are compared. Unusual Kikuchi band patterns are found in both a and αT. Structure factor calculations can be used to explain these patterns. Additional higher order Laue zone (HOLZ) rings are seen in αT. Reflections located at n/9[521] are seen in some zero order Laue zones (ZOLZ) in αT. These additional reflections are responsible for the additional HOLZ rings found in αT. Most atomic positions in a and αT are similar. The specific structural feature which causes the additional reflections in αT is not known. Lattice imaging and image calculation will be necessary to determine the exact structure of αT.

Convergent-beam electron diffraction study of strain modulation in GaAs/InGaAs superlattices grown by metal-organic chemical vapour deposition

Abstract Convergent-beam electron diffraction has been used to study strain modulation in GaAs/InGaAs superlattices (6% In and 2% In) in plan-view. Reflections from planes inclined to the interface of the superlattice are split with sidebands, the angular separation of which is related to the modulation periodicity. It is inferred from higher-order Laue zone lines that inclined planes on opposite sides of an interface in GaAs and InGaAs layers are rotated towards and away from the interface as a result of distortion due to coherent matching and local relaxation in regions where the GaAs substrate and buffer layer have been ion-milled away.

Observation of dynamic extinction from high-order Laue zones by convergent beam electron diffraction

The rules for the observation of the dynamical extinction of some kinematically forbidden reflections in convergent beam electron diffraction (CBED), due to the presence of complicated interaction among glide planes or/and screw axes in the crystalline samples, are examined. This interaction is manifested by the characteristics of the sum of the indices h+ k+ l, which will show up when the high-order Laue zones (HOLZ) are involved in CBED work. Then the complication of interpreting possible dynamic extinction arises. A procedure is therefore devised to decompose a multi-scattering process into basic kinematical scattering steps which can then be rigorously analyzed on the basis of the well-documented knowledge of X-ray crystallography, without relying on the sometimes deceptive intuitive argument. The usefulness of the decomposition table is demonstrated with two examples.

Thickness dependence of the intensities of the 200 forbidden reflections in the TiBe2 diamond type structure

It is interesting to note that for the diamond type structure of Si, Ge and diamond, the forbidden {200} reflections in the exact <100> orientation diffraction pattern cannot be seen. In contrast, we also note a standing controversy over the structure of the MgAl2O4, spinel. Its structure was determined long ago by x-ray powder method as Fd3m (the diamond type). However, its electron diffraction pattern taken in the <100> orientation shows weak {200} reflections, which are taken as evidence that the spinel should have the space group F43m (the blende type), rather than Fd3m. Others speculate that these {200} reflections result from the high order Laue zone (HOLZ) reflections, and the spinel should be Fd3m. Nevertheless, still others think that these analyses are not conclusive. We have carefully studied the space group of TiBe2 using the convergent beam electron diffraction technique, and unambiguously demonstrated that its space group must be Fd3m.

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.

Zone-axis critical voltages and large-angle electron diffraction at 200–400 kV

This paper reviews aspects of electron diffraction with electron microscopes operating at voltages in the range 200–400 kV. each of which appears rich with possibilities for future development. Critical voltage measurements have mostly been made under conditions of one-dimensional diffraction. Recent developments have revealed a wide variety of two-dimensional critical voltages which occur within the operating range of modern instruments and offer the prospect of accurate and useful crystallographic information. Three recent examples include distinguishing titanium carbide from titanium nitride, measurement of the local composition of lead tin telluride and the stoichiometry of high-temperature supercondctors. Large-angle convergent-beam electron diffraction is becoming an invaluable tool in revealing how intensity arrives in a particular Bragg reflection, and hence in solving crystallographic problems. It is also proving extremely effective in studying crystal defects and interfaces. In particular, its application in plan-view samples to the detailed study of quantum well structures and to local variations which occur offers the prospect of routine investigation of epi-layers on a macroscopic scale. The challenge involved in electron diffraction studies is often that of finding a way of bringing physical insight to the interpretation of experimental results. The means of doing this may vary greatly, depending on whether a question of symmetry is involved, or an interpretation is required for a high resolution image or for some higher-order Laue zone (HOLZ) lines in a convergent-beam electron diffraction pattern. In this review I will concentrate on some recent results of electron diffraction obtained using accelerating voltages of up to 300 kV, which depend for their interpretation on the Bloch wave formulation of dynamical theory or its coexistence with kinematical diffraction theory.

Interpretation of electron channeling patterns from non-centrosymmetric crystals

Some of the errors associated with the use of the kinematic or plane-wave approximation to simulate higher-order Laue zone (HOLZ) lines observed in convergent-beam electron diffraction patterns are discussed. The applicability of a proposed formula for estimating the required correction is tested on a variety of materials (with atomic number ranging from 14 to 69) and zone axes. The formula is straightforward to compute and involves only the structure factors of the material; it does not require a many-beam dynamical calculation. It is shown that the formula works best for weak axes. The effects of composition on HOLZ line positions can thus be readily estimated.

Relative lattice parameter measurement of submicron quaternary (InGaAsP) device structures grown on InP substrates

With x-ray diffraction techniques, it is possible to routinely measure lattice parameters to several parts in 104 for thin-film samples. However, measurements of lattice parameter changes for quaternary device structures several microns in width are not usually feasible with x-ray diffraction techniques. For this reason, transmission electron microscopy has been used to determine the position of higher-order Laue zone lines within convergent-beam electron diffraction patterns from thin foil cross sections of planar quaternary layers grown on InP substrates. A calibration curve has been generated which describes the position of higher-order Laue zone lines as a function of the lattice parameter determined from x-ray diffraction measurements. For the active quaternary region of an elecro-optical device structure, it is shown that ths calibration procedure may be sensitive to a relative change in lattice parameter as small as ±2 parts in 104.

Evidence for very high order laue zone (VHOLZ) lines in CBED patterns

It is well known that High Order Laue Zone (HOLZ) line analysis is a powerful tool to study lattice parameter changes due to local chemical composition and microstrain, in addition to determining crystal symmetry. One of the first approaches described by Ecob et al for indexing the HOLZ reflections does not simulate all the observed HOLZ lines. Therefore a more complete computer program for indexing all the observed HOLZ reflections based on kinematical conditions has been developed using the visibility criterion originally developed for Kossel lines. This approach is easy and more accurate. With this technique we have been able to identify very high order Laue zone lines (>3rd order) in low symmetry orientations and index them.Figs, la and lb are computer simulations which show the indexed HOLZ reflections for the second order (SOLZ) and fourth order Laue zone (FOROLZ) in the <116> zone axis. The corresponding defect HOLZ lines in the transmitted disk from pure Al are shown along with computer-simulated patterns for both the SOLZ and FOROLZ in Figs. 2a and 2b respectively.

The usefulness of high index low symmetry zone axes for holz line analysis

Researchers have tended to use high symmetry zone axes (e.g. <111> <114>) for High Order Laue Zone (HOLZ) line analysis since Jones et al reported the origin of HOLZ lines and described some of their applications. But it is not always easy to find HOLZ lines from a specific high symmetry zone axis during microscope operation, especially from second phases on a scale of tens of nanometers. Therefore it would be very convenient if we can use HOLZ lines from low symmetry zone axes and simulate these patterns in order to measure lattice parameter changes through HOLZ line shifts. HOLZ patterns of high index low symmetry zone axes are shown in Fig. 1, which were obtained from pure Al at -186°C using a double tilt cooling holder. Their corresponding simulated HOLZ line patterns are shown along with ten other low symmetry orientations in Fig. 2. The simulations were based upon kinematical diffraction conditions.

The energy dependence of axial coherent bremsstrahlung in the high-voltage electron microscope

Coherent bremsstrahlung (CB) emitted by 200 to 1000 keV electrons traversing oriented silicon crystal targets has been detected using a high voltage electron microscope equipped with an energy dispersive x-ray spectrometer. In this energy range there 1s a strong dependence on the relativistic properties of the Incident electrons: β = v/c varies from about 0.69 (E = 200 keV) to 0.94 (E = 1 MeV); whereas in higher energy accelerator CB experiments β remains close to unity and the variation of any particular peak energy with respect to E is small.This work concentrates on the detection of the “type B” CB which arises from “juddering” of the electron beam as it traverses successive planes of atoms and is prominent 1n directions transverse to the beam. These spectra exhibit harmonics, peak energies which are Integral multiples of a basic value, which can be ascribed to Umklapp processes in successively higher order Laue zones (H0LZ) of the reciprocal lattice.

Analysis of a displacive superlattice in nickel arsenide

Abstract The structural analysis by convergent-beam electron diffraction is described for a weak orthorhombic superlattice observed in both mineral and synthetic samples of NiAs. The three equivalent directions for the commensurate wavevector, q = ⅓(a∗ + b∗), defined a domain structure within the hexagonal subcell. Within a single domain, the symmetry around the c axis was reduced from 6mm to 2mm. The internal structure of higher-order Laue-zone reflections in diffraction patterns recorded at 100 K was used to associate a specific phonon eigenvector or condensed soft mode with the atomic displacement pattern.

Detection and measurement of local distortions in a semiconductor layered structure by convergent-beam electron diffraction

It is shown that local tetragonal distortion in a Si Ge0.05Si0.95 strained-layered structure can be detected and quantified from analyses of the high-order Laue zone lines which are present in the bright-field disks of [001] convergent-beam electron diffraction patterns. The detection of a tetragonal distortion is based on symmetry arguments, whereas the quantification requires a detailed analysis which is based on computer simulated patterns, assuming a kinematical approximation of the scattering process and including surface relaxation. The result of this quantitative analysis is in good agreement with the tetragonal distortion which is predicted by isotropic elasticity theory.

Convergent beam electron diffraction

AbstractIn convergent-beam electron diffraction (CBED) a highly convergent electron beam is focussed on to a small (⩽50 nm) area of the sample. Instead of the diffraction spots that are obtained in the back focal plane of the objective lens with parallel illumination in conventional selected-area electron diffraction, CBED produces discs of intensity. The point group can be determined uniquely from the symmetry within the individual discs and the overall pattern. In order to determine the point group, it is usually necessary to record a number of CBED patterns with the electron beam aligned along different zone axes, but sometimes only one, high-symmetry pattern is required. The positions of reflections in higher-order Laue zones can be used to identify the crystal system and lattice type and to detect the presence of certain glide planes. The repeat along the zone axis that is parallel to the beam can be calculated from the diameters of the Laue zones. Hence the presence ofpolymorphs can be detected. Doubly-diffracted discs in CBED often contain a ‘line of dynamic absence’, the orientation of this line with respect to the symmetry seen in the bright field disc allows the symmetry element responsible for it (glide plane or screw diad) to be identified. This allows 191 of the 230 space groups to be uniquely identified. The measurement of specimen thickness, extinction distance and cell parameters are also briefly discussed.