Dynamical Theory Of Electron Diffraction Research Articles

EBSD patterns simulating multilayer twins based on dynamical theory of electron diffraction.

Electron backscatter diffraction (EBSD) can be employed to determine crystal structures but has not been used alone to identify defects at the atom scale due to the lack of understanding of the EBSD patterns generated by various structure defects. In the present work, the EBSD patterns of FCC-Fe with 9-layer, 6-layer and 3-layer twin structures are simulated, respectively, using the revised real space (RRS) method and compared with the counterpart of perfect crystals. Our results show that when the electron beam is incident along a direction parallel to the twin plane, the pattern appears symmetrical with respect to the corresponding Kikuchi band of the twin plane, and the diffraction details within the Kikuchi band also exhibit symmetry with respect to the middle line of the Kikuchi band. Moreover, the overall clarity of the patterns decreases, and the pattern becomes more blurred with increasing the distance from the Kikuchi band corresponding to the twin plane. By contrast, the incident electron beam along the direction perpendicular to the twin plane results in diffraction superposition of the matrix region and the shear region, which shows twofold rotational symmetry with respect to the Kikuchi pole corresponding to the normal to the twin plane. In addition, some extra Kikuchi bands appear in the EBSD patterns due to the long-period structures of the multilayer twins. As the number of multilayer twins decreases, the number of extra Kikuchi bands decreases and the area of the blurring pattern increases. The correlation between twin structures and EBSD patterns provides theoretical insights for identifying twin structures by the EBSD technique.

Electron channelling contrast imaging of dislocations in a conventional SEM

Dislocations in shock loaded tantalum single crystals were imaged using both transmission electron microscope (TEM) and electron channelling contrast image (ECCI) in a scanning electron microscope with a conventional backscattered electron detector. The results were compared with backscattered electron intensity profiles across dislocations calculated via the dynamic theory of electron diffraction. A one-to-one correspondence between ECCI and TEM is established. High voltage and low index reflections should be used to obtain the highest dislocation contrast and greatest imaging depth.

Comparison of EBSD patterns simulated by two multislice methods.

The extraction of crystallography information from electron backscatter diffraction (EBSD) patterns can be facilitated by diffraction simulations based on the dynamical electron diffraction theory. In this work, the EBSD patterns are successfully simulated by two multislice methods, that is, the real space (RS) method and the revised real space (RRS) method. The calculation results by the two multislice methods are compared and analyzed in detail with respect to different accelerating voltages, Debye-Waller factors and aperture radii. It is found that the RRS method provides a larger view field of the EBSD patterns than that by the RS method under the same calculation conditions. Moreover, the Kikuchi bands of the EBSD patterns obtained by the RRS method have a better match with the experimental patterns than those by the RS method. Especially, the lattice parameters obtained by the RRS method are more accurate than those by the RS method. These results demonstrate that the RRS method is more accurate for simulating the EBSD patterns than the RS method within the accepted computation time.

Error analysis of the crystal orientations and disorientations obtained by the classical electron backscatter diffraction technique

The fidelity – that is, the error, precision and accuracy – of the crystallographic orientations and disorientations obtained by the classical two-dimensional Hough-transform-based analysis of electron backscatter diffraction patterns (EBSPs) is studied. Using EBSPs simulated based on the dynamical electron diffraction theory, the fidelity analysis that has been previously performed using the patterns simulated based on the theory of kinematic electron diffraction is improved. Using the same patterns, the efficacy of a Fisher-distribution-based analytical accuracy measure for orientation and disorientation is verified.

Point-group sensitive orientation mapping of non-centrosymmetric crystals

We demonstrate polarity-sensitive orientation mapping of non-centrosymmetric phases by Electron Backscatter Diffraction (EBSD). The method overcomes the restrictions of kinematic orientation determination by EBSD, which is limited to the centro-symmetric Laue-groups according to Friedel's rule. Using polycrystalline GaP as an example, we apply a quantitative pattern matching approach based on simulations using the dynamical theory of electron diffraction. This procedure results in a distinct assignment of the local orientation according to the non-centrosymmetric point group of the crystal structure under investigation.

Synthesis of AlFe Intermetallic Nanoparticles by High-Energy Ball Milling

ABSTRACTIn this investigation, the chemical and microstructural characteristics of nanostructured AlFe intermetallic produced by high-energy ball milling have been explored. High purity elemental powders were used as the starting material. The ball milling was carried out at room temperature using a SPEX-8000 mixer/mill. The structure, morphology and compositions of the powders were obtained using X-ray diffraction patterns (XRD), scanning and transmission electron microscopy (STEM). High resolution electron microscopy observations have been used in the nanostructured materials characterization. The structural configurations have been explored through comparisons between experimental HREM images and theoretically simulated images obtained with the multislice method of the dynamical theory of electron diffraction.

Chirality determination of quartz crystals using electron backscatter diffraction.

We demonstrate the determination of crystal chirality using electron backscatter diffraction (EBSD) in the scanning electron microscope. The chirality of α-quartz as a space-group-dependent property is verified via direct comparison of experimental diffraction features to simulations using the dynamical theory of electron diffraction.

Three-dimensional measurement of composition changes in InAs/GaAs quantum dots

We present a transmission electron microscope (TEM) analysis of InAs/GaAs quantum dots (QDs) which have been subject to thermal annealing. Annealing produces a significant shift in infrared detector response to longer wavelengths, indicating changes in QD size, composition, or both. A three-dimensional reconstruction of an 'average' QD is obtained by combining compositionally-sensitive dark field 002 TEM images of many QDs, followed by fitting to a structural model assuming cylindrical symmetry. Errors in compositional measurements are estimated, and the validity of the model is assessed by TEM image simulations using 2-beam dynamical electron diffraction theory. As-grown material exhibits an increasing concentration of In towards the top of the QDs, whereas annealed material shows diffusion of indium from the upper part of the QD towards the sides and base. There is no measurable change in the position of the outer interface of the QD.

Site-Specific Recoil Diffraction of Backscattered Electrons in Crystals

A novel diffraction effect in high-energy electron backscattering is demonstrated: the formation of element-specific diffraction patterns via nuclear recoil. For sapphire (Al(2)O(3)), the difference in recoil energy allows us to determine if an electron scattered from aluminum or from oxygen. The angular electron distribution obtained in such measurements is a strong function of the recoiling lattice site. These element-specific recoil diffraction features are explained using the dynamical theory of electron diffraction. Our observations open up new possibilities for local, element-resolved crystallographic analysis using quasielastically backscattered electrons in scanning electron microscopy.

AlN Nanorods synthesized by a Mechanothermal Process

ABSTRACTWell-crystallized AlN nanorods have been produced by mechanical milling and subsequent annealing treatment of the milling powders (mechanothermal process). High purity AlN powders were used as the starting material. Mechanical milling was carried out in a vibratory SPEX mill for 30 h, using vials and balls of silicon nitride. The annealing treatment was carried out at 1200 ºC for 10 min. The characterization of the samples was performed by X-ray diffractometry and transmission electron microscopy (TEM). TEM observations indicated that the synthesized nanorods consisted of 30 nm in diameter and 100 nm in length. High resolution electron microscopy observations have been used in the structural characterization. AlN nanorods exhibit a well-crystallized structure. The growing direction of the nanorods is close to the [001] direction. The structural configurations have been explored through comparisons between experimental HREM images and theoretically simulated images obtained with the multislice method of the dynamical theory of electron diffraction.

Principles of depth‐resolved Kikuchi pattern simulation for electron backscatter diffraction

This paper presents a tutorial discussion of the principles underlying the depth-dependent Kikuchi pattern formation of backscattered electrons in the scanning electron microscope. To illustrate the connections between various electron diffraction methods, the formation of Kikuchi bands in electron backscatter diffraction in the scanning electron microscope and in transmission electron microscopy are compared with the help of simulations employing the dynamical theory of electron diffraction. The close relationship between backscattered electron diffraction and convergent beam electron diffraction is illuminated by showing how both effects can be calculated within the same theoretical framework. The influence of the depth-dependence of diffuse electron scattering on the formation of the experimentally observed electron backscatter diffraction contrast and intensity is visualized by calculations of depth-resolved Kikuchi patterns. Comparison of an experimental electron backscatter diffraction pattern with simulations assuming several different depth distributions shows that the depth-distribution of backscattered electrons needs to be taken into account in quantitative descriptions. This should make it possible to obtain more quantitative depth-dependent information from experimental electron backscatter diffraction patterns via correlation with dynamical diffraction simulations and Monte Carlo models of electron scattering.

Quantitative measurements of Kikuchi bands in diffraction patterns of backscattered electrons using an electrostatic analyzer

Diffraction patterns of backscattered electrons can provide important crystallographic information with high spatial resolution. Recently, the dynamical theory of electron diffraction was applied to reproduce in great detail backscattering patterns observed in the scanning electron microscope (SEM). However, a fully quantitative comparison of theory and experiment requires angle-resolved measurements of the intensity and the energy of the backscattered electrons, which is difficult to realize in an SEM. This paper determines diffraction patterns of backscattered electrons using an electrostatic analyzer, operating at energies up to 40 keV with sub-eV energy resolution. Measurements are done for different measurement geometries and incoming energies. Generally a good agreement is found between theory and experiment. This spectrometer also allows us to test the influence of the energy loss of the detected electron on the backscattered electron diffraction pattern. It is found that the amplitude of the intensity variation decreases only slowly with increasing energy loss from 0 to 60 eV.

Correlation between Auger Intensity and Wave-Field Intensity for Si(001)2*2-Al Surface

According to dynamical theory of electron diffraction, the incident electron density distribution, or “wave-field”, was calculated for a parallel-dimer structure of Si(001)2×2-Al surface on the condition of medium-energy electron diffraction (MEED). The surface structure and the calculated method were confirmed to be effective by the rocking-curve analysis of diffracted beam intensity. The wave-field at the surface is very sensitive to changes in diffraction conditions, such as the incident glancing angle. The Al(LMM) Auger electron intensity emitted from the Si(001)2×2-Al surface during MEED incident beam rocking, that is named beam rocking Auger electron spectroscopy (BRAES), has been found to be correlated to the calculated wave-field intensity on the Al atomic rows. The BRAES profile of adsorbate Al(LMM) differs from that of substrate Si(LVV). [DOI: 10.1380/ejssnt.2009.97]

High-energy photoelectron diffraction: model calculations and future possibilities

We discuss the theoretical modeling of x-ray photoelectron diffraction (XPD) with hard x-ray excitation at up to 20 keV, using the dynamical theory of electron diffraction to illustrate the characteristic aspects of the diffraction patterns resulting from such localized emission sources in a multilayer crystal. We show via dynamical calculations for diamond, Si and Fe that the dynamical theory predicts well the available current data for lower energies around 1 keV, and that the patterns for energies above about 1 keV are dominated by Kikuchi bands, which are created by the dynamical scattering of electrons from lattice planes. The origin of the fine structure in such bands is discussed from the point of view of atomic positions in the unit cell. The profiles and positions of the element-specific photoelectron Kikuchi bands are found to be sensitive to lattice distortions (e.g. a 1% tetragonal distortion) and the position of impurities or dopants with respect to lattice sites. We also compare the dynamical calculations with results from a cluster model that is more often used to describe lower energy XPD. We conclude that hard XPD (HXPD) should be capable of providing unique bulk-sensitive structural information for a wide variety of complex materials in future experiments.

TEM analysis of planar defects in β-SiC

Abstract This paper reports on a transmission electron microscopy (TEM) and high resolution TEM (HRTEM) investigation of the extended defects in β-SiC grown on Si (0 0 1) substrates by CVD. The main defects observed were stacking faults and twins. Stacking fault contrast can be explained by using the dynamical theory of electron diffraction. It was found that in β-SiC, stacking faults on inclined {1 1 1} planes exhibit complementary and symmetrical bright-field and dark-field fringe images. This observation is ascribed to the low anomalous absorption ratio of Bloch waves in SiC. Excellent agreement was found between experimental and simulated inclined stacking fault images in β-SiC. Narrow dark bands on {1 1 1} planes viewed edge-on generated streaks but no additional spots in selected area diffraction patterns. HRTEM revealed that these defects are extrinsic stacking faults. Models for the introduction and evolution of the lattice defects observed will be presented.

Structural analysis and shape-dependent catalytic activity of Au, Pt and Au/Pt nanoparticles

Metallic nanoparticles of Au, Pt and Pt/Au have been synthesized using a chemical reduction approach. The structural characterization of these metallic nanoparticles has been carried out using conventional transmission electron microscopy (TEM) and high resolution transmission electron microscopy (HR-TEM) techniques. HR-TEM images of Pt nanoparticles reveal their fcc-like structures, in the [103] and [011] orientations. However, in case of Au, the main structures are fcc-like and decahedral morphologies with five-fold symmetry axes. The structure of the gold nanoparticles was verified through their theoretically-simulated images, using a multislice approach of the dynamical theory of electron diffraction. These small particles have been used as electrocatalysts in Nafion membranes for fuel cell applications. The electrochemical characterization of the membranes shows that the Pt dispersion gives best performance for fuel cell applications.

Sum rules for electron energy loss near edge spectra

We derive four sum-rule expressions for spectra measured in electron energy loss near edge structure experiments. These sum rules permit the determination of spin and orbital magnetic moments, spin-orbit interaction, and number of states, analogously to the sum rules of x-ray magnetic circular dichroism. The derivation of the sum rules is based on dynamical electron diffraction theory and the properties of the mixed dynamic form factor. The accuracy of the sum rules is tested by a complete evaluation of the thickness-dependent electron energy loss spectra for iron, cobalt, and nickel crystals. We find that the sum rules reproduce both spin and orbital moments with very good accuracy. Our results provide a foundation for the use of the energy loss magnetic chiral dichroism technique as a quantitative probe of element-specific magnetic properties.

Synthesis of gold nanoparticles with different atomistic structural characteristics

A chemical reduction method was used to produce nanometric gold particles. Depending on the concentration of the main reactant compound different nanometric sizes and consequently different atomic structural configurations of the particles are obtained. Insights on the structural nature of the gold nanoparticles are obtained through a comparison between digitally-processed experimental high-resolution electron microscopy images and theoretically-simulated images obtained with a multislice approach of the dynamical theory of electron diffraction. Quantum molecular mechanical calculations, based on density functional theory, are carried out to explain the relationships between the stability of the gold nanoparticles, the atomic structural configurations and the size of nanoparticles.

Electron resonances in VLEED from Cu(111)

The sensitivity of the VLEED I–V curves to the shape and the position of the barrier is shown for the image- type surface barriers. For demonstration and comparison with experimental data the intensities of specularly reflected electron beams from Cu(111) are computed by dynamical theory of electron diffraction. Image plane position changes and modifications of the saturation shape of the surface barrier induce pronounced changes in the I–V curves calculated with the image-type barrier.

Preparation of AlFe Nanoparticles by Mechanical Alloyed Technique

Small metallic particles (1-3 nm) have been obtained using mechanical alloying techniques. Analytical techniques such as scanning electron microscopy have been used for the morphological and chemical characterization of the AlFe alloyed powders. B, Ni and Ti have been explored as reinforced elements to the initial AlFe mixture. X-ray diffraction patterns and transmission electron microscopy (TEM) techniques have been employed for the structural characterization of the small metallic particles. Theoretical simulations based on molecular dynamics have been used to interpret some of the experimental structural results. Furthermore, theoretical simulations of HREM images based on the dynamical theory of electron diffraction have also been obtained and comparisons with the experimental results have been carried out. The complementary analyses determined that the produced clusters are basically AlFe alloyed nanoparticles immersed in a matrix and with multiple defected structures.