Contribution of electron precession to the study of perovskites displaying small symmetry departures from the ideal cubic ABO3 perovskite: applications to the LaGaO3 and LSGM perovskites

Electron microscopy and electron diffraction are well adapted to the study of the fine‐grained, faulted pure and doped LaGaO₃ and LSGM perovskites in which the latter is useful for fuel cell components. Because these perovskites display small symmetry departures from an ideal cubic ABO₃ perovskite, many conventional electron diffraction patterns look similar and cannot be indexed without ambiguity. Electron precession can easily overcome this difficulty mainly because the intensity of the diffracted beams on the precession patterns is integrated over a large deviation domain around the exact Bragg condition. This integrated intensity can be trusted and taken into account to identify the ‘ideal’ symmetry of the precession patterns (the symmetry which takes into account both the position and the intensity of the diffracted beams). In the present case of the LaGaO₃ and LSGM perovskites, the determination of the ‘ideal’ symmetry of the precession patterns is based on the observation of weak ‘superlattice’ reflections typical of the symmetry departures. It allows an easy and sure identification of any zone axes as well as the correct attribution of hkl indices to each of the diffracted beams. Examples of applications of this analysis to the characterizations of twins and to the identification of the space groups are given. This contribution of electron precession can be easily extended to any other perovskites or to any crystals displaying small symmetry departures.     

A precession electron diffraction study of α, β phases and Dauphiné twin in quartz

Precession electron diffraction is used to distinguish between the hexagonal β high-temperature and the trigonal α low-temperature phases of SiO₂ quartz. The structures just differ by a kink of the SiO₄ tetrahedra arranged along spiraling chains, which induces a loss of the two-fold axis and subsequent twinning in the low-temperature phase. Conventional selected-area electron diffraction (SAED) does not enable the phases distinction since only the intensity of reflections is different. It becomes possible with precession that reduces the dynamical interactions between reflections and makes their intensity very sensitive to small variations of the electron structure factors. Distinction between the twinned individuals in the low-temperature phase is then easily made and the twin law is characterized using stereographic projections. The actual symmetry of precessed zone axis patterns is also examined in detail. Using dynamical intensity simulations, it is shown that under certain thickness conditions, the diffraction class symmetry can be observed on selected area patterns that are to be used in the case of beam sensitive materials such as quartz.     

The relative intensities of electron diffraction maxima in mixed rare-earth oxides

The relative intensities of electron diffraction maxima from yttrium aluminium perovskite were analysed in terms of the atomic scattering contribution to the structure factors and in terms of double diffraction. It has been shown that double diffraction influences the visible intensity between diffraction spots in electron diffraction patterns to a greater extent than does the magnitude of the structure factor. A direct consequence of this is that the intensity of diffraction maxima can increase when a specimen is tilted off an exact zone axis.     

Zone-axis diffraction patterns by the “Tanaka” method

The “Tanaka” method is one of several techniques that make it possible to obtain zone-axis electron diffraction patterns in a transmission electron microscope without the restriction in the field of view that limits normal convergent-beam diffraction patterns. The method employs a convergent-beam of electrons focused to a probe in a plane that does not coincide with the specimen. The selected area aperture can then be used to eliminate all but one of the diffracted beams to obtain the desired pattern. Practical details of operation and values of operating parameters are discussed. The Tanaka method is a useful addition to the techniques available to the electron microscopist, especially since no instrumental modification is required.     

Investigation and use of plasmon losses in energy-filtering transmission electron microscopy

The electron spectroscopic imaging (ESI), diffraction (ESD) and different types of electron energy-loss spectroscopy (EELS) modes in an energy-filtering transmission electron microscope can all be used for the investigation and analytical use of plasmon losses. Shifts of plasmon losses caused by differences in composition can be detected with an accuracy of 0.1 eV by parallel-recorded EELS (PEELS). The dispersion of plasmon losses and the cut-off angle θ_c can be observed by angle-dispersive EELS and by recording spectra at different scattering angles θ. ESD patterns with a selected energy window width of 1 eV enable the dispersion and its anisotropy to be imaged by characteristic intensity distributions between the primary beam and the first Bragg diffracted beams. The ESI mode can be used for the selective imaging of precipitates and for the investigation of the excitation volume of plasmons in small particles.     

Fortran source listing for simulating three-dimensional convergent beam patterns with absorption by the Bloch wave method

The FORTRAN source code is given for a computer program that calculates the two-dimensional intensity distribution in convergent-beam transmission electron microdiffraction (CBED) patterns from perfect crystals. The program uses the eigenvalue or Bloch-ware method. It allows three-dimensional dynamical diffraction, and so includes all higher-order Laue zone effects without approximation. No symmetry reduction is included. The program accepts noncentrosymmetric or centrosymmetric crystal structures and allows absorption corrections to be included. It uses the “EISPACK” subroutines for the diagonalisation of a general complex matrix. Up to 100 CBED disks may be included. The code is also available via “Bitnet”.     

New approach for the dynamical simulation of CBED patterns in heavily strained specimens

A new method for the dynamical simulation of convergent beam electron diffraction (CBED) patterns is proposed. In this method, the three-dimensional stationary Schrödinger equation is replaced by a two-dimensional time-dependent equation, in which the direction of propagation of the electron beam, variable z, stands as a time. We demonstrate that this approach is particularly well-suited for the calculation of the diffracted intensities in the case of a z-dependent crystal potential. The corresponding software has been developed and implemented for simulating CBED patterns of various specimens, from perfect crystals to heavily strained cross-sectional specimens. Evidence is given for the remarkable agreement between simulated and experimental patterns.     

Progress toward structure determination

Convergent-beam electron diffraction provides more precise measurements of diffracted intensity than the traditional method of selected-area diffraction. The intensity is recorded at well-defined beam directions for each reflection in the pattern within disks defined by the incident cone of rays. Measurements relating to structure factors or parameters can be arranged in different ways: intensities at the zone axis position; Kossel line profiles or integrated intensities across Kossel lines; conditions for vanishing contrast at a Kossel line (e.g., critical voltage); separation between Kossel line segments at intersections. Examples of application to refinement of structure parameters (zone axis intensities) and structure factor determination (Kossel line methods) are given. The relation of these magnitudes to theory is discussed, especially for the Kossel line methods. These are described in terms of effective Fourier potentials or gaps at the Bloch-wave dispersion surface. Use of the methods for refinement of structure parameters and structure factors is reviewed with special attention to recent developments. This is seen along two lines: (1) extended scope for the more accurate methods in order to cover larger unit cells and (2) better precision in measurements of intensities.     

LACDIF, a new electron diffraction technique obtained with the LACBED configuration and a C(s) corrector: comparison with electron precession

By combining the large-angle convergent-beam electron diffraction (LACBED) configuration together with a microscope equipped with a C(s) corrector it is possible to obtain good quality spot patterns in image mode and not in diffraction mode as it is usually the case. These patterns have two main advantages with respect to the conventional selected-area electron diffraction (SAED) or microdiffraction patterns. They display a much larger number of reflections and the diffracted intensity is the integrated intensity. These patterns have strong similarities with the electron precession patterns and they can be used for various applications like the identification of the possible space groups of a crystal from observations of the Laue zones or the ab-initio structure identifications. Since this is a defocused method, another important application concerns the analysis of electron beam-sensitive materials. Successful applications to polymers are given in the present paper to prove the validity of this method with regards to these materials.     

Electron precession microdiffraction as a useful tool for the identification of the space group

The possible space groups of a crystal can be identified from a few zone axis microdiffraction patterns provided the position (and not the intensity) of the reflections on the patterns is taken into account. The method is based on the observation of the shifts and the periodicity differences between the reflections located in the first-order Laue zone (FOLZ) with respect to the ones located in the zero-order Laue zone (ZOLZ).
Electron precession microdiffraction patterns display more reflections in the ZOLZ and in the FOLZ than in the conventional microdiffraction patterns and this number increases with the precession angle. It is shown, from the TiAl example given in the present study, that this interesting feature brings a strong beneficial effect for the identification of the possible space groups since it becomes very easy to identify unambiguously the FOLZ/ZOLZ shifts and periodicity differences. In addition, the diffracted intensity on the precession patterns is the integrated intensity and this intensity can also be used to identify the Laue class.     

Electron beam damage of behenic acid films

The rate of fading of electron diffraction patterns of behenic acid monolayer crystals as well as multilayer crystals was measured at 100 kV at room temperature to investigate the dependence of beam damage on specimen thickness. The diffracted intensities for monolayers and double layers decreased nearly exponentially with electron exposure; however, the intensities for multilayers were unchanged during initial electron exposures, often increased temporarily and then decreased with electron exposure. The critical dose, D_e, defined as the dose at which the diffracted intensity falls to 1/e of its initial value, was 1.0 electrons/Ų for the monolayers, 1.8 electrons/Ų for the double layers and more for multilayers. These results lead to the conclusion that D_e for behenic acid increases nearly linearly with specimen thickness in the range of about 25–100 Å for dose rate of 0.1–2 electrons/Ų min.     

Dynamical simulations of zone axis electron channelling patterns of cubic silicon carbide

We have observed and simulated energy-dependent intensity distributions in electron channelling patterns (ECP) of cubic silicon carbide (3C SiC) which were recorded close to the (111) zone axis. The kinetic energies used were in the range from 4 to 8 keV, covering the low-energy region of the ECP technique. We explain the observed patterns by dynamical many beam simulations using a bloch wave approach for the diffraction of the incoming beam and the forward-backward-approximation for the backscattering of the electrons. The dynamical simulations reproduce the experimental patterns very well. It is found that higher-order Laue zone reflections are responsible for the strong energy sensitivity of the intensity distributions.     

Dynamical electron diffraction simulation for non‐orthogonal crystal system by a revised real space method

In the transmission electron microscopy, a revised real space (RRS) method has been confirmed to be a more accurate dynamical electron diffraction simulation method for low‐energy electron diffraction than the conventional multislice method (CMS). However, the RRS method can be only used to calculate the dynamical electron diffraction of orthogonal crystal system. In this work, the expression of the RRS method for non‐orthogonal crystal system is derived. By taking Na₂Ti₃O₇ and Si as examples, the correctness of the derived RRS formula for non‐orthogonal crystal system is confirmed by testing the coincidence of numerical results of both sides of Schrödinger equation; moreover, the difference between the RRS method and the CMS for non‐orthogonal crystal system is compared at the accelerating voltage range from 40 to 10 kV. Our results show that the CMS method is almost the same as the RRS method for the accelerating voltage above 40 kV. However, when the accelerating voltage is further lowered to 20 kV or below, the CMS method introduces significant errors, not only for the higher‐order Laue zone diffractions, but also for zero‐order Laue zone. These indicate that the RRS method for non‐orthogonal crystal system is necessary to be used for more accurate dynamical simulation when the accelerating voltage is low. Furthermore, the reason for the increase of differences between those diffraction patterns calculated by the RRS method and the CMS method with the decrease of the accelerating voltage is discussed.     

Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness

This paper presents a two-degree-of-freedom (two-DOF) linear encoder which can measure the position along the moving axis (X-axis) and the straightness along the axis vertical to the moving axis (Z-axis) of a precision linear stage simultaneously. The two-DOF linear encoder is composed of a reflective-type scale grating and an optical sensor head. A reference grating, which is identical to the scale grating except the scale length, is employed in the optical sensor head. Positive and negative first-order diffracted beams from the two gratings are superposed with each other in the optical sensor head to generate interference signals. The optical configuration is arranged in such a way that the direction of displacement in each axis can also be detected. A prototype two-DOF linear encoder is designed and constructed. The size of the optical sensor head is about 50 mm (X) × 50 mm (Y) × 30 mm (Z) and the pitch of the grating is 1.6 μm. It has been confirmed that the prototype two-DOF linear encoder has sub-nanometer resolutions in both the X- and Z-axes.     

Diffraction patterns of artificial two-dimensional crystals synthesized in situ in an environmental scanning transmission electron microscope

In this study, we demonstrated the use of electron‐beam‐induced deposition for synthesis of artificial two‐dimensional crystals with an in situ scanning transmission electron microscope. The structures were deposited from W(CO)₆ in an environmental scanning transmission electron microscope on a 30‐nm‐thick Si₃N₄ substrate. We present clear electron beam diffraction patterns taken from those structures. The distance between the diffraction peaks corresponded to the dot spacing in the self‐made surface crystal. We propose using these arrays of dots as anchor points for making artificial crystals for diffraction analysis of weakly scattering or beam‐sensitive molecules such as proteins.     

Effect of sample bending on diffracted intensities observed in CBED patterns of plan view strained samples

Convergent beam electron diffraction is used to study the effect of the sample bending on diffracted intensities as observed in transmission electron microscopy (TEM). Studied samples are made of thin strained semiconductor Ga(1-)(x)In(x)As epitaxial layers grown on a GaAs substrate and observed in plan view. Strong variations of the diffracted intensities are observed depending on the thinning process used for TEM foil preparation. For chemically thinned samples, strong bending of the substrate occurs, inducing modifications of both kinematical and dynamical Bragg lines. For mechanically thinned samples, bending of the substrate is negligible. Kinematical lines are unaffected whereas dynamical lines have slightly asymmetric intensities. We analyse these effects using finite element modelling to calculate the sample strain coupled with dynamical multibeam simulations for calculating the diffracted intensities. Our results correctly reproduce the qualitative features of experimental patterns, clearly demonstrating that inhomogeneous displacement fields along the electron beam within the substrate are responsible for the observed intensity modifications.     

A software tool for automatic analysis of selected area diffraction patterns within Digital Micrograph™

A software package “SADP Tools” is developed as a complementary diffraction pattern analysis tool. The core program, called AutoSADP, is designed to facilitate automated measurements of d-spacing and interplaner angles from TEM selected area diffraction patterns (SADPs) of single crystals. The software uses iterative cross correlations to locate the forward scattered beam position and to find the coordinates of the diffraction spots. The newly developed algorithm is suitable for fully automated analysis and it works well with asymmetric diffraction patterns, off-zone axis patterns, patterns with streaks, and noisy patterns such as Fast Fourier transforms of high-resolution images. The AutoSADP tool runs as a macro for the Digital Micrograph program and can determine d-spacing values and interplanar angles based on the pixel ratio with an accuracy of better than about 2%.     

Lattice distortions in GaN on sapphire using the CBED–HOLZ technique

The convergent beam electron diffraction (CBED) methodology was developed to investigate the lattice distortions in wurtzite gallium nitride (GaN) from a single zone-axis pattern. The methodology enabled quantitative measurements of lattice distortions (α, β, γ and c) in transmission electron microscope (TEM) specimens of a GaN film grown on (0, 0, 0, 1) sapphire by metal-organic vapour-phase epitaxy. The CBED patterns were obtained at different distances from the GaN/sapphire interface. The results show that GaN is triclinic above the interface with an increased lattice parameter c. At 0.85 μm from the interface, α=90°, β=8905° and γ=11966°. The GaN lattice relaxes steadily back to hexagonal further away from the sapphire substrate. The GaN distortions are mainly confined to the initial stages of growth involving the growth and the coalescence of 3D GaN islands.