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Using transmission electron microscopy, we characterised the structures of the boundary caused by the interactions between different twin variants that share the same zone axis in a deformed magnes...

Formation of curious deformation bands has been reported as one of the deformation mechanisms occurring in an Mg-based long-period stacking ordered (LPSO) phase. The origin of the deformation band is still unknown, and the possibility of the deformation kink band and/or the deformation twin has been discussed. To clarify this, the crystallographic nature of deformation bands formed in the LPSO phase was examined by scanning electron microscope–electron backscatter diffraction (SEM-EBSD) pattern analysis. The results were compared to those of the deformation kink bands formed in hcp-Zn and deformation twins formed in hcp-Mg polycrystals. The deformation bands in the LPSO phase was confirmed not to exhibit a fixed crystal orientation relationship with respect to the matrix, different from the case shown in the deformation twin. Instead, the deformation band in the LPSO phase showed three arbitrariness on its crystallographic nature: an ambiguous crystal rotation axis that varied on the [0 0 0 1] zone axis f...

The planar defect structure of coalesced GaN layers fabricated on ordered arrays of nanorods and grown by metal–organic vapour phase epitaxy has been studied using conventional and high-resolution transmission electron microscopy. During the process of coalescence, a boundary was created between two pyramids, where I1-type basal plane stacking faults propagating through the overgrown layers are terminated by Frank-Shockley partial dislocations. According to multislice HRTEM simulations of experimental observed images in the [ ] zone axis, the step-and hairpin-shaped basal prismatic stacking faults with inclined { } plane are consistent with Drum’s structural model, which has a lower formation energy compared with the model proposed by Amelinckx. Based on the observation that there are no stacking faults in the overgrown layers prior to the nanopyramid merging, the mechanism of coalescence induced stacking faults is proposed. This research contributes to the understanding of planar defect formation in III-...

The orientation dependence of ϵ martensite during loading of a polycrystalline austenitic Fe-30Mn-4Si-2Al steel has been investigated by electron backscatter diffraction, emphasising the variant selection rule and plate–plate intersection reactions. Two types of plate–plate intersection reactions, which are characterised by incident shear direction of either 30° or 90° with respect to the intersection axis, were found in the grains along the [001]–[111] directions and [001]–[101] directions, respectively. In the intersecting volume of the latter type reaction, a γ phase rotated 90° from the austenite matrix along the ⟨011⟩ zone axis of the intersecting ϵ plates, which was theoretically predicted by Sleeswyk [A.W. Sleeswyk, Philos. Mag. 7 (1962) p.1597], has been experimentally observed for the first time.

Transmission electron microscopy (TEM) has been instrumental in advancing the field of crystalline defect analysis. Conventional TEM imaging techniques, such as bright field (BF), dark field (DF), and weak beam dark field (WBDF or g–3g) imaging, have been well-documented in the scientific literature, with simulation methods readily available for each. The present contribution highlights the use of a field-emission TEM, operated in scanning transmission electron microscopy mode, as a viable tool for defect analysis. Common techniques such as two-beam diffraction contrast and zone axis imaging are applied to defect analysis; both experimental and computational results are presented. Effects of experimental parameters such as camera length, beam divergence angle, and diffraction aperture placement are also discussed and illustrated by both experimental and computed micrographs of stacking faults.

The microstructure of a Cr buffer layer between a stainless steel (SS) layer, which is a catalytic layer for carbon nanotube growth, and a Si (100) substrate was investigated by high-resolution transmission electron microscopy. The SS film is polycrystalline, and the thickness is not uniform. It was partly covered by a surface Cr2O3 layer. The Cr buffer layer reacted with the Si substrate to form CrSi2. Definite orientation relationships (ORs) between CrSi2 and Si were observed: (OR D) and (OR A). OR D is a new OR found in the CrSi2/Si system. We also found several other new ORs which are similar to OR A and are denoted OR E, OR F, OR G, and OR H. For OR E and OR F, the CrSi2 crystals are rotated, respectively, about 18° and 34° counterclockwise around the zone axis with respect to OR A. For OR G and OR H, the CrSi2 crystals are rotated, respectively, about 35° and 107° clockwise around the zone axis with respect to OR A. These findings not only enrich the crystallography of the CrSi2/Si epitaxial system,...

The late stages of coarsening of coherent solid particles is strongly influenced by the reduction of elastic strain energy. This produces migration and alignment of particles as well as some other effects. In this investigation, the origin of the so-called splitting pattern arrangement of γ′ precipitate particles, an arrangement which has often been interpreted as being due to splitting of a larger particle into smaller ones, has been studied. The two-particle relationship as to whether they are in-phase or out-of-phase is examined by means of a translation order domain analysis of high-resolution electron-microscopy images along a zone axis parallel to [001]. Ni alloys have been used for the investigation including a binary Ni–Al alloy (producing different volume fractions) and two commercial multicomponent alloys with high volume fraction. About 72% of two-particle pairs forming the splitting configuration are in the out-of-phase relationship, indicating that adjacent pairs are randomly formed and that ...

A sharply bimodal lattice site distribution of dilute Cu in both Ni-deficient and Al-deficient beta-phase Ni-Al alloys has been observed in the 63Cu nuclear magnetic resonance (NMR) spectra. These NMR results are correlated with results derived from incoherent channelling patterns (ICPs) formed by variations in characteristic X-ray emission as a function of incident fast electron orientation. Statistical analysis of ICP data, generated near a 210 zone axis, indicates that Cu occupies substitutional sites; Cu is exclusively on the Al sublattice sites in the Al-deficient alloy, whilst the partition ratio of Ni : Al sublattice sites for Cu in the Ni-deficient alloy is about 80 : 20. Comparison of ICP contrast from Cu X-ray emission with ICPs from the host lattice enables the two peaks in the 63Cu NMR spectrum to be individually identified as originating from Cu on Ni sublattice sites, and from Cu on Al sublattice sites. The respective NMR line intensities from the Ni-deficient alloy yields a Ni : Al sublatti...

A new method for analysing antiphase domains using high-resolution electron micrographs is described. A high-resolution electron microscope image taken at a zone axis is treated as the sum of many sets of interference fringes. The analysis extracts the information concerning the variations in the image periodicities as a function of position. In particular, the amplitude and phase variations of these fringes are analysed separately. The amplitude images reveal the antiphase boundaries in a similar way to a conventional dark-field experiment whilst the phase produces images of the translation domains and defines the associated translation vectors. The phase variations can also be related to the strain field associated with the corresponding lattice planes. Experimental images of antiphase boundaries in Cu3Au taken at [001] are used to demonstrate the technique. Antiphase boundaries perpendicular and parallel to the electron beam are characterized. The phase images are used to characterize disorder...

Site occupancy has been determined using the channelling-enhanced microanalysis for a Ni3(Al, Ta) intermetallic compound with the L12-type crystal structure. It is shown that there is a large scattering of data points for [001] beam incidence compared with [111] beam incidence. The reasons for this difference are examined by simulating channelling electron distribution on the Al and Ni columns. It is concluded that the large scattering for the [001] beam incidence is due to the indistinguishable difference between channelling electron intensities on the Al and Ni columns.

A new statistical method for atom location by channelling-enhanced micro-analysis is applied to γ [sbnd] α2 duplex Ti[sbnd]Al based alloys containing ternary element additions of V, Cr, Mn, Ga, Y, Zr, Nb, Mo, La, Hf, Ta and W at the 1 at.% level. Incoherent channelling patterns, formed by the variation in characteristic X-ray emission as a function or orientation, are collected from a number of different zone axes from both phases. Comparisons of experimental patterns with calculated maps for various crystallographic sites indicate that the ternary atoms are incorporated substitutionally in the atomic structure of both the γ and the α2-phases and do not occupy interstitial sites. The crystallographic site distribution of the ternary elements is determined through χ2-minimization techniques, together with quantitative error limits. The structure of the non-stoichiometric α2-phase is investigated by convergent-beam electron diffraction.

Higher-order Laue zone (HOLZ) disc patterns obtained from As-doped and undoped Si have been examined under the exact 011 zone axis orientation at 100 kV. For this orientation, two lines in the HOLZ disc are produced from the intersections of HOLZ reflections, with two branches corresponding to atomic and tunnelling sites of the zeroth-layer dispersion surface. The As atom concentration and its strain contribution can be visibly detected by comparison of the two HOLZ line positions. A simple fitting between experiment and simulation permits a reasonable estimate of the As atom concentration.

A dependent Bloch wave theory for inelastic scattering is adapted to predict back-scattered electron (BSE) contrast from perfect crystals. This is correlated with 300 keV data from a number of zone axes from spinel, chromia, silicon, aluminium and gallium arsenide. This theory is shown to supersede an independent Bloch wave theory for BSE contrast which is incapable of accounting for asymmetry across polar axes. The orientation dependence of thermal dechannelling of fast electrons is shown to be important. The BSE scattering potential is shown to approximate to a delta function scaled by the atomic number squared on each atom.

Thickness extinction fringe profiles are analysed under zone-axis diffraction conditions to characterize strain in Si/SiB multilayers. For the exact (110) zone-axis orientation, three branches of the dispersion surface dominate the 250 keV electron wavefunction, leading to a simplified analysis. Thickness fringe extinction periodicities and shifts associated with strains are interpretable in terms of two dominant interbranch extinction distances.

The response to isothermal recrystallisation and zone recrystallisation of rods of MA 956 and MA 957 has been compared. Isothermal recrystallisation produced equiaxed millimetre sized grains in MA 957, whereas MA 956 had grains of high aspect ratio. This is attributed to an anisotropic distribution of oxide particles in MA 956. In both alloys the initial strong 〈110〉 fibre texture is transformed into textures lying on the 〈001〉–〈111〉 zone axis. A discrete zone recrystallisation interface could not be formed in MA 956 under the range of conditions investigated. This may be accounted for by an anisotropic boundary pinning force. This results in small transverse velocities and also a different zone recrystallisation texture in MA 956 from that in MA 957.MST/1860

The homogeneous decomposition of a Co-1 at.% Co alloy at 823K has been investigated by bright-field-zone-axis-incidence transmission electron microscopy. The new method allows detection of Co precipitates with radii r≤ 1 nm, independent of their position in the foil, and the contrast of the particles is straightforwardly related to their real dimension. So we were able to measure the particle density N v, the mean radius r, the distribution function f(r) of the radii and the pair correlation function PCF(R) of the particle spacings R with high accuracy. The data have been compared with the predictions of a modified Langer-Schwartz theory. Best correspondence is obtained with a value of 240 mJ m−2 for the interfacial energy per unit area of Cu-Co. The spacings R of the particles showed no significant regularity as expected from an initial spinodal-like precursor fluctuation of the Co concentration.

Two fast-electron quantum states are highly excited for crystal orientations close to the Si zone axis, manifesting themselves as pairs of lines associated with each high-order Laue zone (HOLZ) reflection. The electron wave-vector k is determined from absolute positions of deficit lines in the zeroth-order beam, where full account is taken of dynamically induced displacements compared with positions determined from kinematic (geometrical) theory. Geometrie results approximate experiment provided that k is modified by Δk, equivalent to a voltage shift ΔE. The two excited Bloch states provide an independent assessment of Δk. Changes in HOLZ line position with inereasing temperature are due to delocalization of the projected potential and corresponding shifts in eigenvalues. The displacement of HOLZ lines due to thermal lattice dilation is three times smaller than shifts due to delocalization of the elastic potential. A nominal 300 kV accelerating voltage of a Philips CM30 electron microscope i...

A general formulation for the six-dimensional lattice of the decagonal phase has been utilized for systematically deducing its geometrical consequences on the three-dimensional structures obtained by taking a section of the hyperlattice. Indexing of diffraction patterns has been accomplished on this basis. A zone axis rule and an interplanar spacing formula have been derived. Structures have been proposed for the decagonal phases with different reciprocal space periodicities and having P105/mcm symmetry.

It has been proposed that bright-field imaging of coherent spherical precipitates under zone axis incidence would give improved resolution in the strain contrast compared with the weak-beam dark-field imaging. We observed the strain contrast from coherent Co-precipitates in Cu-Co alloys, and simulated the images on the basis of many-beam dynamical electron diffraction, taking into account the elastic anisotropy. Zone axis incidence such as [001] or [001] considerably reduces the effective extinction distance of the transmitted beam, and suppresses the intensity oscillation with foil thickness, in comparison with a conventional two-beam condition. The contrast in the bright-field images is straightforwardly related to the precipitate geometry. Individual precipitates are well resolved in the image when the number density of precipitates is fairly high. It has been demonstrated that the imaging under zone axis incidence is quite useful to understanding of microstructures in phase transformation in ...

A high-energy permanent magnet, whose nonmagnetic structure belongs to the space group P6/m mm, has been used to study the magnetic effect on symmetry determination by convergent-beam electron diffraction (CBED) patterns. At the [0001] zone axis, along which the magnetization of the domains is aligned, the symmetry of CBED patterns remains 6mm as if the specimen were nonmagnetic. However, at the zone axis, the mirror planes contained by the c axis were absent in the zero-order disks even though the whole pattern appeared to have 2mm symmetry. By looking into the interaction between the electron beam and the magnetic field produced by the specimen, it was found that the magnetic effect of the specimen was zero in the first-order approximation when the electron beam was along the [0001] direction, and was maximized when the electron beam was parallel to the basal plane. The apparent 2mm symmetry in the whole pattern of zone axis indicates that diffraction is overwhelmed by the Coulombic potential i...

An investigation of the form of electron diffraction zone axis patterns has been made for zone axes where the projected potentials may be regarded as arrays of identical, approximately cylindrically symmetric, potential wells. Close-packed, approximately close-packed, square and rectangular arrangements of the potential wells are considered (such as occur for the 〈111〉, 〈110〉 and 〈100〉 axes of f.c.c. and b.c.c. crystals for example). The observed patberns are interpreted in terms of dispersion surfaces obtained by matrix calculations. A simple development of the patterns is observed in the first Brillouin zones if the patterns are arranged according to their proximity to the second critical voltage. A method for measuring the second critical voltage is described and discussed and the importance of diagonalizing complex matrices near this degeneracy is emphasized. The previously reported approximate equivalence of small voltage and thickness changes to zone axis patterns (Tatlock and Steeds 1973) ...

The idea of a string integral as a measure of the number of bound states, or the strength of a crystal potential when projected along a zone axis was introduced by Ozorio de Almeida (1973). We here explore its utility in distinguishing the various stages in the sequence of patterns filling the first Brillouin zone which was described in the preceding paper (Shannon and Steeds 1977) and, in particular, for locating the second critical voltage. The positions of the accidental degeneracies and of the eigenvalues having minimum attenuation coefficients (Doyle and Berry 1973) are evaluated in several cases in relation to the top of the potential wells. Critical voltages higher than the second are investigated in a few cases. One of these has a simple projected potential in the sense described by Shannon and Steeds (1977) (Mo 〈111〉) and others have more complex potentials (2H MoS2[0001], diamond structure 〈110〉). The order of the bound states of different symmetry within the potential wells for the Mo ...

Three-dimensional, fine distributions of electron current density in a molybdenum crystal are examined by the many-beam dynamical theory of electron diffraction for electrons incident parallel to the principal zone axes. It is found that the two-dimensional distribution in the transverse plane oscillates along the depth direction, and that a highly localized distribution around the rows of atoms and an almost flat distribution appears alternatively with definite periods of depth. The effect of the localized current density on the damage production is discussed by introducing the “effective current ratio”, J eff which is defined as the ratio of the local current density at the rows of atoms to the mean current density for electrons incident parallel to the zone axis. The values J eff for the incidence of 1 MeV electron are found to increase in the order of the (111), (001) and (110) directions. The energy dependence J eff is also examined for the (001), (110) and (111) axial cases respectively.

A new method for measuring a two-dimensional set of kinematic intensities from electron diffraction patterns is described, where a beam with a large convergence angle is focused parallel to a zone axis on to the crystal. If the convergence semi-angle is adjusted to match the angular radius, α1 of the first-order Laue zone, then all electrons diffracted by planes in layer n of the reciprocal lattice are confined to an annulus around the zone-axis direction with inner and outer radii equal to αn and an αn+1, respectively. As the convergence semi-angle of the incident beam is increased from zero to α1, the set of g vectors in layer n which satisfy the Brag condition expands from a circle with radius R n(≈ n 1/2 R 1) to an annulus with radii equal to R n+1±R 1. The measured intensities for electrons diffracted around a Si〈114〉 axis are shown to fit kinematic calculations, where reflections with either odd or even indices are separated into two distinct sets.

New experimental results are reported for type B coherent bremsstrahlung (CB) radiation from kilovolt electrons traversing thin crystals in zone axis orientations, obtained using an electron microscope and energy dispersive X-ray detector, approximately at right angles to the beam. These results are interpreted using the three-dimensional Bloch wave theory of multiple coherent electron scattering, which predicts coherent bremsstrahlung (‘weak-beam radiation’), channelling radiation (‘Pendellosung radiation’) and combinations thereof. Absent CB peaks are observed from Laue zones in which all structure factors are zero. Doppler broadening is found to make the observation of channelling radiation satellites on CB peaks difficult. Closed-form expressions for ‘resonant’ CB are given.

Kikuchi patterns from single crystals of magnesium oxide have been studied by electron microscopy at various accelerating voltages between 500 kV and 1 MV. In each case, the incident beam falls on the crystal near a zone axis [012] so that many non-systematic reflections were either strongly excited or not excited. In this paper it is shown that the critical voltage effect is very sensitive to the crystal orientation and, even when accidental reflections are weakly excited, the second-order Kikuchi lines vanish at a very different voltage than in the systematic case. Apart from this new value, a minimum intensity along the second-order Kikuchi lines and a reversal of the asymmetric contrast of the mid-line can be observed. These effects appear in the diffraction pattern at various distances of the systematic row, depending on the accelerating voltage and the excitation of the non-systematic reflections. They can be understood from the many-beam dynamical theory, and the theoretical profiles of th...

The many-beam dynamical theory of electron diffraction is used to simulate zone axis patterns in molybdenite. It is shown that all the main features of the complex [0001] patterns can be generated with a 61 beam calculation, and that marked changes in the patterns with accelerating voltage and specimen thickness can be explained by the form of the dispersion surfaces.

A zone-axis critical voltage is reported in the [001] transmission electron diffraction pattern of the superconducting ceramic La1.8Sr0.2CuOy. Experimentally, this is found to occur at 95 kV; simplified theoretical calculations indicate that the critical voltage is so highly sensitive to the crystal potential that it changes by > 5 kV for a 2.5% variation in oxygen vacancy content. In principle, this technique can now be used to measure the oxygen stoichiometry to within ±2.5% from a ∼ 1 nm region in a well characterized single-phase region, and should also provide a sensitive measure of the La stoichiometry. Problems with the absolute quantification of the method are discussed, and it is concluded that the major application of this effect lies in comparative measurements of stoichiometry variations from sample to sample, and compositional inhomogeneities within a single sample.

Observations of both dark-field and bright-field convergent-beam discs were performed close to the zone-axis critical voltages (ZACV) of f.c.c. stainless steel , Si and Cr zone axes. A switching of asymmetric contrast was observed in the dark-field convergent-beam electron diffraction (CBED) discs of each zone-axis pattern. In the case of stainless steel, the switch of asymmetric contrast occurred at different accelerating voltages depending on the choice of diffracted beam. This effect can be interpreted by the structure of the Bloch wave dispersion surfaces. In the case of the Si ZACV, the switching of asymmetric contrast was observed in both bright- and dark-field CBED discs at the ZACV, and the results facilitated a precise determination of the ZACV. The asymmetric contrast was also observed in the dark-field discs of the Cr axis and again facilitated a precise determination of the ZACV.

The observation of dark-field convergent-beam discs of the zeroth-order Laue zone (ZOLZ) reflections and higher-order Laue zone (HOLZ) reflection discs was carried out around the chromium Cr zone-axis critical voltage (ZACV), to find the best method of measuring the ZACV precisely. A reversal of asymmetric contrast was observed in some of the dark-field convergent-beam discs at the critical voltage, and this was interpreted by dynamical diffraction theory. The HOLZ reflections showed notable effects around the ZACV over a range of more than 100 kV. This effect was interpreted by the quasi-kinematical theory of three-dimensional diffraction. The experimental results revealed a method capable of measuring the ZACV precisely, and the ZACV of Cr was measured with similar precision to that attainable in the systematic critical voltage (SCV) case.

A reasonable first approximation to the crystal potential experienced by high-energy electrons incident close to the [0001] axis of trigonal or hexagonal transition-metal dichalcogenides is a hexag...

High-resolution electron microscopic studies are reported on the nature of the complex domain patterns which occur in the room temperature phase of the hexagonal bronze KWNb2O9. Two-dimensional lattice images reveal the domain wall configurations, with walls having virtually zero thickness, containing steps (kinks) of atomic dimensions. Wall rearrangements, following kink propagation under the influence of the electron beam, are also described. Symmetrical zone axis images, for extremely thin edges of the specimens, reveal directly the nature of the (W, Nb) atom displacements responsible for the hexagonal component of the superstructures occurring throughout five phases, which exhibit a series of structural phase transitions, including ferroelectric phases, in the temperature range 270-560°C.

THE relationship between crack growth and plastic deformation in ionic crystals has been elucidated recently by Stokes and Li (1962) and by Tattersall and Clarke (1962) who have demonstrated the anisotropic nature of crack growth from subcritical to critical Griffith size. Stokes and Li (1962) studied the extension of subcritical cracks in NaCl under tension and proved that surface microcracks extend anisotropically into the crystal, the direction of crack growth lying parallel to the zone axis of the active, orthogonal slip bands. They attributed the anisotropic growth pattern of the microcracks to the influence of slip bands, which resist crack propagation across the slip band, but aid propagation parallel to the band.