Higher-order Laue Zone Research Articles

On the origin of diffuse intensities in fcc electron diffraction patterns.

Interpreting diffuse intensities in electron diffraction patterns can be challenging in samples with high atomic-level complexity, as often is the case with multi-principal element alloys. For example, diffuse intensities in electron diffraction patterns from simple face-centred cubic (fcc) and related alloys have been attributed to short-range order1, medium-range order2 or a variety of different {111} planar defects, including thin twins3, thin hexagonal close-packed layers4, relrod spiking5 and incomplete ABC stacking6. Here we demonstrate that many of these diffuse intensities, including [Formula: see text]{422} and [Formula: see text]{311} in ⟨111⟩ and ⟨112⟩ selected area diffraction patterns, respectively, are due to reflections from higher-order Laue zones. We show similar features along many different zone axes in a wide range of simple fcc materials, including CdTe, pure Ni and pure Al. Using electron diffraction theory, we explain these intensities and show that our calculated intensities of projected higher-order Laue zone reflections as a function of deviation from their Bragg conditions match well with the observed intensities, proving that these intensities are universal in these fcc materials. Finally, we provide a framework for determining the nature and location of diffuse intensities that could indicate the presence of short-range order or medium-range order.

Electronic and nanoscale structures of metal oxyhalide intergrowth photocatalysts

Multimetal oxyhalide intergrowths show promise for photocatalytic water splitting. However, the relationships between intergrowth stoichiometry and their electronic and nanoscale structures are yet to be identified. This study investigates Bi4TaO8Cl–Bi2GdO4Cl intergrowths and demonstrates that stoichiometry controls the tilting of [TaO6] octahedra, influencing the bandgap of the photocatalyst and its valence and conduction band positions. To determine how the [TaO6] octahedral tilting in the intergrowths manifests as a function of intergrowth stoichiometry, we investigated changes in crystal symmetry by analyzing features arising at the higher order Laue zone (HOLZ) of convergent-beam electron diffraction patterns. Higher Ta content intergrowths displayed a more intense outer HOLZ ring compared to lower Ta content intergrowths, indicating transformation from P21cn (orthorhombic) to P4/mmm (tetragonal). This finding suggests that more distortion occurs along the ⟨001⟩ directions of the crystal than the ⟨100⟩ and ⟨010⟩ directions. This variation directly impacts the electronic structure, affecting both conduction and valence band energy levels. By combining ultraviolet photoelectron spectroscopy, UV-visible diffuse reflectance spectroscopy, and electron energy loss spectroscopy, the absolute band positions of the intergrowths were determined. Agreement between the bandgaps obtained via ensemble and nanoscale measurements indicates nanoscale homogeneity of the electronic structure. Overall, the integrated approach establishes that the bandgap energy increases with increasing Ta content, which is correlated with the crystal symmetry and [TaO6] octahedral tilting. Broadly, the modular nature of intergrowths provides building block layers to tune octahedral tilting within perovskite layers for manipulation of optoelectronic properties.

Imaging Structural Phase Transitions with Higher Order Laue Zones Using 4D-STEM.

Imaging Structural Phase Transitions with Higher Order Laue Zones Using 4D-STEM.

Twinning in hydrous wadsleyite: Symmetry relations, origin, and consequences

AbstractTwins in hydrous wadsleyite were detected by polarized-light microscopy and characterized with transmission electron microscopy techniques, including precession selected area electron diffraction and large-angle convergent beam diffraction. By inspecting diffracted intensities for high-order Laue zones, we found the symmetry of our hydrous wadsleyite samples to be reduced to monoclinic with respect to the orthorhombic symmetry of most anhydrous wadsleyite samples. Twinned domains in hydrous wadsleyite share the (122) plane as a composition plane and are related to each other by a twofold rotation around a twin axis parallel to [212] or by reflection on (122). The twin axis and twin plane in wadsleyite correspond to the <101> directions and the {101} planes of ringwoodite, respectively. The twin operations exchange the c* and the [120]* directions of wadsleyite, both of which correspond to the directions of the cubic a axes in ringwoodite. Based on our analysis of symmetry relations and pseudo-symmetry in wadsleyite, we conclude that the twins formed during crystal growth under quasi-hydrostatic conditions in the presence of a hydrous fluid. Twinning in wadsleyite may affect the physical properties and deformation behavior of wadsleyite as well as the phase transition to ringwoodite in the Earth’s mantle transition zone.

Determining lattice parameters from two electron diffraction patterns

Lattice parameters are the fundamental quantities to describe a crystal structure, but the X-ray or neutron diffraction technique can determine only the averaged structure. Local lattice parameters can be determined from two zone-axis electron diffraction patterns (ZAPs) and the overall tilt angle, but the crystal needs to be oriented at the exact zone axis. This is a time-consuming transmission electron microscopy operation and largely limits structure determination of nanocrystallites. Here, a new method is proposed to reconstruct the 3D reciprocal cell and determine the lattice parameters from two ZAPs, one of which contains a high-order Laue zone (HOLZ) ring. The validity of the method was verified on both a low-symmetry monoclinic structure and a high-symmetry cubic crystal. The advantage of the method is that the accuracy of the lattice parameters measured is largely dependent on the HOLZ ring, which will considerably simplify the transmission electron microscopy operation. In this work, both the HOLZ-based method and the angle-based method were integrated into the DigitalMicrograph plugin UnitCell Tools—Two Patterns. With the help of this program, the lattice parameters of a crystal can be determined from two electron diffraction patterns efficiently and precisely.

Very-High Dynamic Range, 10,000 Frames/Second Pixel Array Detector for Electron Microscopy.

Precision and accuracy of quantitative scanning transmission electron microscopy (STEM) methods such as ptychography, and the mapping of electric, magnetic, and strain fields depend on the dose. Reasonable acquisition time requires high beam current and the ability to quantitatively detect both large and minute changes in signal. A new hybrid pixel array detector (PAD), the second-generation Electron Microscope Pixel Array Detector (EMPAD-G2), addresses this challenge by advancing the technology of a previous generation PAD, the EMPAD. The EMPAD-G2 images continuously at a frame-rates up to 10 kHz with a dynamic range that spans from low-noise detection of single electrons to electron beam currents exceeding 180 pA per pixel, even at electron energies of 300 keV. The EMPAD-G2 enables rapid collection of high-quality STEM data that simultaneously contain full diffraction information from unsaturated bright-field disks to usable Kikuchi bands and higher-order Laue zones. Test results from 80 to 300 keV are presented, as are first experimental results demonstrating ptychographic reconstructions, strain and polarization maps. We introduce a new information metric, the maximum usable imaging speed (MUIS), to identify when a detector becomes electron-starved, saturated or its pixel count is mismatched with the beam current.

Niggli reduction and Bravais lattice determination

A new algorithm has been developed and coded in DigitalMicrograph (DM) to reduce a three-dimensional primitive cell to the Niggli cell and further convert to the Bravais-lattice unit cell. The core of this algorithm is the calculation of the three shortest non-coplanar vectors to compose the reduced cell. The reduced cell is converted into the real-space reduced cell and then to the Bravais-lattice unit cell. The symmetry-constrained unit cell is, in turn, converted back into the real-space reduced cell, the reciprocal reduced cell and the reciprocal primitive cell. The DM package demonstrates superior numerical stability and can tolerate large uncertainties in the experimentally measured input primitive cell, making it especially suitable for electron diffraction analysis. Additionally, the DM package can be used to calculate various crystallographic parameters including Bravais-lattice plane indices, zone-axis indices, tilt angles and the radius of the high-order Laue zone ring, thus facilitating the correct determination of the Niggli cell and the Bravais lattice.

UnitCell Tools, a package to determine unit-cell parameters from a single electron diffraction pattern.

Electron diffraction techniques in transmission electron microscopy (TEM) have been successfully employed for determining the unit-cell parameters of crystal phases, albeit they exhibit a limited accuracy compared with X-ray or neutron diffraction, and they often involve a tedious measurement procedure. Here, a new package for determining unit-cell parameters from a single electron diffraction pattern has been developed. The essence of the package is to reconstruct a 3D reciprocal primitive cell from a single electron diffraction pattern containing both zero-order Laue zone and high-order Laue zone reflections. Subsequently, the primitive cell can be reduced to the Niggli cell which, in turn, can be converted into the unit cell. Using both simulated and experimental patterns, we detail the working procedure and address some effects of experimental conditions (diffraction distortions, misorientation of the zone axis and the use of high-index zone axis) on the robustness and accuracy of the software developed. The feasibility of unit-cell determination of the TiO2 nanorod using this package is also demonstrated. Should the parallel-beam, nano-beam and convergent-beam modes of the TEM be used flexibly, the software can determine unit-cell parameters of unknown-structure crystallites (typically >50 nm).

Atomic resolution HOLZ-STEM imaging of atom position modulation in oxide heterostructures

It is shown that higher order Laue zone (HOLZ) rings in high energy electron diffraction are specific to individual columns of atoms, and show different strengths, structure and radii for different atom columns along the same projection in a structure. An atomic resolution 4-dimensional STEM dataset is recorded from a <110> direction in a perovskite trilayer, where only the central LaFeO3 layer should show a period doubling that gives rise to an extra HOLZ ring. Careful comparison between experiment and multislice simulations is used to understand the origins of all features in the patterns. A strong HOLZ ring is seen for the La-O columns, indicating strong La position modulation along this direction, whereas a weaker ring is seen along the O columns, and a very weak ring is seen along the Fe columns. This demonstrates that atomic resolution HOLZ-STEM is a feasible method for investigating the 3D periodicity of crystalline materials with atomic resolution.

Fast Pixelated Detectors in Scanning Transmission Electron Microscopy. Part II: Post-Acquisition Data Processing, Visualization, and Structural Characterization.

Fast pixelated detectors incorporating direct electron detection (DED) technology are increasingly being regarded as universal detectors for scanning transmission electron microscopy (STEM), capable of imaging under multiple modes of operation. However, several issues remain around the post-acquisition processing and visualization of the often very large multidimensional STEM datasets produced by them. We discuss these issues and present open source software libraries to enable efficient processing and visualization of such datasets. Throughout, we provide examples of the analysis methodologies presented, utilizing data from a 256 × 256 pixel Medipix3 hybrid DED detector, with a particular focus on the STEM characterization of the structural properties of materials. These include the techniques of virtual detector imaging; higher-order Laue zone analysis; nanobeam electron diffraction; and scanning precession electron diffraction. In the latter, we demonstrate a nanoscale lattice parameter mapping with a fractional precision ≤6 × 10−4 (0.06%).

Atomic structure and crystallography of joints in SnO2 nanowire networks

Joints of three-dimensional (3D) rutile-type (r) tin dioxide (SnO2) nanowire networks, produced by the flame transport synthesis (FTS), are formed by coherent twin boundaries at (101)r serving for the interpenetration of the nanowires. Transmission electron microscopy (TEM) methods, i.e. high resolution and (precession) electron diffraction (PED), were utilized to collect information of the atomic interface structure along the edge-on zone axes [010]r, [111]r and superposition directions [001]r, [101]r. A model of the twin boundary is generated by a supercell approach, serving as base for simulations of all given real and reciprocal space data as for the elaboration of three-dimensional, i.e. relrod and higher order Laue zones (HOLZ), contributions to the intensity distribution of PED patterns. Confirmed by the comparison of simulated and experimental findings, details of the structural distortion at the twin boundary can be demonstrated.

Geometry determination and refinement in the rotation electron diffraction technique

The necessary parameters (rotation axis, incident electron beam direction and beam tilt path) in order to describe the diffraction geometry in the Rotation Electron Diffraction (RED) method during data collection are determined and refined. These parameters are prerequisites for the subsequent calculations of excitation errors, sg, for zero (ZOLZ) or higher order Laue zones (HOLZ) reflections. Comparison with simulated results, for a CoP3 thermoelectric crystal, shows excellent agreement between the two approaches -calculated and simulated. In addition to their determination, a thorough refinement methodology for the incident electron beam direction and beam tilt path has been applied, too, based on Kikuchi lines of HOLZ reflections. Incorporation of the refined excitation error values can be considered both in theoretical calculations for diffracted beam intensities, based on the Bloch wave method, as well as in deducing integrated intensities from experimental rocking curves. The methodology described in this study is quite indispensable, as it forms an essential step for performing dynamical calculations in RED, enabling thus enhanced accuracy in structural parameter clarification. The latter is especially important in the case of thermal factors refinement for e.g. thermoelectrics, which are imperative for material properties’ evaluation.

The application of convergent beam electron diffraction (CBED) analysis on transformation-induced plasticity (TRIP) steels.

Convergent beam electron diffraction (CBED) in transmission electron microscopy (TEM) was applied to determine local carbon concentrations in low-carbon transformation-induced plasticity (TRIP) steels. High-order Laue-zone (HOLZ) lines were experimentally obtained for comparison with simulation results. A new procedure for calculating carbon content is thus proposed. Retained austenite (RA) is classified into three types by morphology; the relationship between the carbon content and the corresponding RA morphology is discussed based on CBED results. Furthermore, results of X-Ray diffractometry measurements are also used for comparison.

Determination of the structural phase and octahedral rotation angle in halide perovskites

A key to the unique combination of electronic and optical properties in halide perovskite materials lies in their rich structural complexity. However, their radiation sensitive nature limits nanoscale structural characterization requiring dose efficient microscopic techniques in order to determine their structures precisely. In this work, we determine the space-group and directly image the Br halide sites of CsPbBr3, a promising material for optoelectronic applications. Based on the symmetry of high-order Laue zone reflections of convergent-beam electron diffraction, we identify the tetragonal (I4/mcm) structural phase of CsPbBr3 at cryogenic temperature. Electron ptychography provides a highly sensitive phase contrast measurement of the halide positions under low electron-dose conditions, enabling imaging of the elongated Br sites originating from the out-of-phase octahedral rotation viewed along the [001] direction of I4/mcm persisting at room temperature. The measurement of these features and comparison with simulations yield an octahedral rotation angle of 6.5°(±1.5°). The approach demonstrated here opens up opportunities for understanding the atomic scale structural phenomena applying advanced characterization tools on a wide range of radiation sensitive halide-based all-inorganic and hybrid organic-inorganic perovskites.

Self-interference of split HOLZ line (SIS-HOLZ) for z-dependent atomic displacement measurement: Theoretical discussion

A characteristic of the majority of semiconductors is the presence of lattice strain varying with the nanometer scale. Strain originates from the lattice mismatch between layers of different composition deposited during epitaxial growth. Strain can increase the mobility of the charge carriers by the band gap reduction. So, measuring atomic displacement inside crystals is an important field of interest in semiconductor industry. Among all available transmission electron microscopy techniques offering nano-scale resolution measurements, convergent beam electron diffraction (CBED) patterns show the highest sensitivity to the atomic displacement. Higher Order Laue Zone (HOLZ) lines split by small non-uniform variations of lattice constant allowing to measure the atomic displacement through the crystal. However, it could only reveal the atomic displacement in two dimensions, i.e., within the x–y plane of the thin film of TEM specimen. The z-axis atomic displacement which is along the path of the electron beam has been missing. This information can be obtained by recovering the phase information across the split HOLZ line using the self-interference of the split HOLZ line (SIS-HOLZ). In this work, we report the analytical approach used to attain the phase profile across the split HOLZ line. The phase profile is studied for three different atomic displacement fields in the Si substrate at 80nm away from its interface with Si/Si0.8Ge0.2 superlattices.

Aberration-corrected self-interference of split higher order Laue zone line for measuring the z-dependent strain profile

Abstract

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 Na2 Ti3 O7 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.

Mapping of Strain Fields in GaAs/GaAsP Core-Shell Nanowires with Nanometer Resolution.

We report the nanoscale quantification of strain in GaAs/GaAsP core-shell nanowires. By tracking the shifting of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction patterns, we observe unique variations in HOLZ line separation along different facets of the core-shell structure, demonstrating the nonuniform strain fields created by the heterointerface. Furthermore, through the use of continuum mechanical modeling and Bloch wave analysis we calculate expected HOLZ line shift behavior, which are directly matched to experimental results. This comparison demonstrates both the power of electron microscopy as a platform for nanoscale strain characterization and the reliability of continuum models to accurately calculate complex strain fields in nanoscale systems.

The Presence of Higher-Order Laue Zone Intensities and the Relrod Effect in Cubic Metals in the Transmission Electron Microscope

The Presence of Higher-Order Laue Zone Intensities and the Relrod Effect in Cubic Metals in the Transmission Electron Microscope

Quantifying mean inner potential of ZnO nanowires by off-axis electron holography

Off-axis electron holography has been used to quantitatively determine the mean inner potential of ZnO. [0001] grown ZnO nanowires with hexagonal cross-sections were chosen as our samples because the angle between the adjacent surfaces is 120°, as confirmed by electron tomography, so the entire geometry of the nanowire could be precisely determined. The acceleration voltage of the transmission electron microscope was accurately calibrated by convergent beam electron diffraction (CBED)–higher-order Laue-zone (HOLZ) analyses. ZnO nanowires were tilted away from zone-axis to avoid strong dynamical diffraction effect, and the tilting angles were determined by CBED patterns. Our experimental data found a mean inner potential of ZnO as 14.30±0.28V.