CBED contrast in the lower order Laue zone

Contrast in a systematic arrangement of lower order Laue zone (LOLZ) beams is reported and analysed using a Bloch wave description. Observations are reported for hexagonal barium ruthenium zirconate (Ba4Ru3ZrO12) and barium ruthenium titanate (Ba3Ti2RuO9), both near the c-axis orientation. The specific scattering dynamics invoked by this diffraction geometry may have novel uses in the exploration of crystallographic parameters.

Channelling effects in atomic resolution STEM

A Bloch wave theory for incoherent scattering of an incident plane wave has proved successful in predicting the fine detail in 2-D zone axis channelling patterns formed by ADF, BSE and characteristic X-ray detection in beam rocking mode. A previously published example of polarity determination of GaAs by channelling contrast is compared with simulations in order to illustrate the applicability of the theory. Modification of boundary conditions for a focused coherent probe allows lattice-resolution incoherent contrast based on ADF and EELS detection as well as X-ray emissions to be catered for within a similar theoretical framework. Mixed dynamic form factors constitute an integral part of this theory, where quantum-mechanical phase is a core issue. Simulations of lattice-resolution ADF and EELS are discussed with reference to various zone axis projections of GaAs. Issues of single versus double channelling conditions, and local versus nonlocal interactions, are discussed in relation to X-ray, ADF and EELS detection.

Lattice-resolution contrast from a focused coherent electron probe. Part II

In the previous paper, boundary conditions matching the probe to the crystal wave function in scanning transmission electron microscopy were applied by matching the whole wave function across the boundary. It is shown here how that approach relates to previous Bloch wave formulations using (phase-linked) plane wave boundary conditions for wave vectors implied by the range of transverse momentum components in the incident probe. Matching the whole wave function across the boundary, and including a suitably fine mesh in the reciprocal space associated with the crystal to allow matching of transverse momentum components within the probe, leads to a structure matrix A containing many elements which would normally be excluded for plane wave incidence. For perfect crystals, the A-matrix may be block diagonalised. This leads to a considerable increase in the computational efficiency of the model and yields important insights into the physics of convergent probes in perfect crystals-reciprocity in coherent imaging and the small aperture limit for coherent and incoherent contrast are considered. The numerical equivalence of the incoherent lattice contrast calculated in this Bloch wave method and the multislice method using mixed dynamic form factors will be demonstrated. Comparison between both these methods and the frozen phonon model, a prevalent multislice method for annular dark field simulation which has the theoretical advantage of handling double channelling, will be made.

Lattice-resolution contrast from a focused coherent electron probe. Part I

To develop a Bloch wave framework for lattice-resolution contrast derived from coherent or incoherent scattering of an electron probe focused onto a crystal, boundary conditions which influence the propagation of an arbitrarily distorted coherent electron probe are addressed. These boundary conditions are particularly relevant for a probe focused within a unit cell, and lead to a general theory which hinges on Bloch wave excitation amplitudes being written as a function of beam position and focus. Whereas antisymmetric Bloch states are not excited for an incident plane wave at an exact zone axis orientation, these states may be strongly excited depending on probe focus and position within the unit cell. Equations for both coherent and incoherent lattice image contrast in scanning transmission electron microscopy are derived for any detector configuration in the Bloch wave framework. An equivalent expression amenable to evaluation via multislice techniques is also described. It is shown explicitly how mixed dynamic form factors for incoherent scattering should be taken into account for annular dark field or backscattered electron detectors, as well as for characteristic losses detected by X-ray emissions or by electron energy loss spectroscopy. A background contribution from "absorbed" electrons is included in the theory. The contribution of cross-talk from neighbouring columns to incoherent contrast is examined within the context of this theoretical framework.

HOLZ line analysis of lattice parameters in magnesium alloys

A method of refining lattice parameters from deficit higher-order Laue zone (HOLZ) line data from large angle convergent beam electron diffraction (LACBED) data is presented, relying on distances between nearest neighbour intersections alone in order to minimize effects of distortion over the field of view. Use is made of a dynamical correction deltak to the fast electron wavevector k for kinematic analysis. This correction term is shown to depend on the specific HOLZ beam under consideration, as well as the zone axis and eigenvalue associated with the branch index of the relevant dispersion surface. This method is applied to analysis of data from magnesium alloys, where momentum filtering induced by the LACBED method facilitates HOLZ contrast from a relatively low index zone axis (where contrast is not detectable with conventional CBED), and contrast is enhanced at elevated temperatures from a higher index zone axis. Although the accuracy of refined lattice parameters from these sets of data is shown to be no better than 0.1%, it is felt that issues arising out of the analysis may be of some interest, particularly since these are non-ideal specimens. Full eigen-state analysis of the fast electron wavefunction is presented, and issues related to the influence of the dispersion surface on deficit HOLZ line behaviour are discussed.

Location of Zn within the Mg12(LaxCe1-x) lattice by X-ray incoherent channelling patterns

Systematic electron diffraction studies on intermetallic precipitates formed within a lightweight Mg-RE-Zn alloy (RE = La or Ce) identify these to be of structural type Mn(12)Th (space group I4/mmm). Analytical electron microscopy yields an overall composition of Mg(12)(La(x)Ce(1-x)) with x ~ 0.43, with 1 at.% Zn incorporated within the lattice. Variations in characteristic X-ray emission rates, as an electron beam is rocked near zone-axis orientations, are used to form two-dimensional channelling patterns, termed X-ray incoherent channelling patterns. This channelling contrast enables a specific sublattice site that is occupied by Zn to be unambiguously identified within the Mg(12)RE lattice. The particular sublattice site is denoted by the Wyckoff letter f, and is one of the three different Mg sublattice sites f, i and j. Of these three sites, the Wigner-Seitz cell that is centred on the f sublattice site has the largest Mg-RE interatomic distance, and therefore the f site is expected to be favoured for accommodating the substitution of a larger Zn atom.

Strain-induced symmetry breakdown in HOLZ lines from L1(2) titanium tri-aluminides

Energy filtered CBED patterns of the Cr-stabilized L1(2) phase of a titanium tri-aluminide alloy reveal deficit higher order Laue zone (HOLZ) lines in the zeroth order diffraction disk, for which the expected 4-mm symmetry is significantly broken in the <001> projection. This apparent break of symmetry may be explained by the presence of lattice strains of order 10(-3). Effects of strain-induced lattice distortions on HOLZ line symmetries are calculated by an introduction of rhombohedral, tetragonal or monoclinic distortions to the cubic unit cell. It is shown how tensile and shear components of strain affect the overall HOLZ line symmetries in different ways.

Effects of Diffraction on the (e,2e) Reaction in Crystals

An expression is derived for the (e, 2e) differential cross section of a crystal, with allowance for dynamic diffraction of both the incident and outgoing electrons, all of which are assumed to be fast. Conditions for unique momentum determination on the one hand or for maximum enhancement of the (e,2e) signal on the other are discussed.

Lattice Images of Solid Xenon Precipitates in Aluminum at Room Temperature

Small solid precipitates (bubbles) of xenon in an aluminum matrix have been formed by ion implantation. Lattice images of this room-temperature inert gas solid were obtained using high-resolution phase-contrast electron microscopy. Many bubbles showed a high degree of crystalline perfection, but regions of defective crystallinity were observed in several cases.