Calculation Of Electron Diffraction Intensities Research Articles

A complete comparison of simulated electron diffraction patterns using different parameterizations of the electron scattering factors

The steadily improving experimental possibilities in instrumental resolution as in sensitivity and quantization of the data recording put increasingly higher demands on the precision of the scattering factors, which are the key ingredients for electron diffraction or high-resolution imaging simulation. In the present study, we will systematically investigate the accuracy of fitting of the main parameterizations of the electron scattering factor for the calculation of electron diffraction intensities. It is shown that the main parameterizations of the electron scattering factor are consistent to calculate electron diffraction intensities for thin specimens and low angle scattering. Parameterizations of the electron scattering factor with the correct asymptotic behavior (Lobato and Dyck [5], Kirkland [4], and Weickenmeier and Kohl [2]) produce similar results for both the undisplaced lattice model and the frozen phonon model, except for certain thicknesses and reflections.

Charge density determination in icosahedral AlPdMn quasicrystal using quantitative convergent beam electron diffraction

Charge density distribution in icosahedral AlPdMn quasicrystal has been studied on a single-crystal specimen by using quantitative convergent beam electron diffraction (QCBED) technique. The QCBED systematic row method was used in the refinement of structure factors. To refine the low-order structure factors, the wave-mechanical formulation of electron diffraction dynamical theory was used in the calculation of electron diffraction intensities for the quasicrystal in fitting the experimental intensity line scan profiles. The shapes of atomic surfaces (occupation domains) were described with symmetry-adapted series of surface harmonics. An iterative procedure was used in determination of structure factors of the quasicrystal. The structure factors of nine strongest symmetry inequivalent reflections according to X-ray diffraction experiment were refined with QCBED technique. The average of refinement results for a given reflection performed on several CBED patterns, which were slightly different in orientation and sample thickness, and on different line scans, was taken as the value of structure factor for the reflection. The obtained structure factors for electrons were transformed into X-ray structure factors with Mott formula. The bonding charge density map for the quasicrystal was constructed with the obtained nine structure factors. Assuming that the atoms are spheres, the gain or loss of electrons for different atoms were calculated. It shows that identical atoms can have different valences at different kinds of positions. The bonding charge is localized along certain directions.

A method to determine long-range order parameters from electron diffraction intensities detected by a CCD camera

To determine long-range order parameters from electron diffraction intensities, the authors have developed a CCD camera system to detect precisely electron diffraction intensities, a method for quickly and precisely measuring specimen thickness, and a computer programming to calculate long-range order parameters from the ratio of superlattice and fundamental diffraction intensities. Thickness variation over a diffraction area is taken into consideration in the calculation of electron diffraction intensities on the basis of the multi-slice method, and long-range order parameters are calculated by the successive approximation method. The absorptive form factors are also calculated from experimental data of diffraction intensities by parameter fitting, and the effect of absorption on the calculation of long-range order parameters is examined. The values of Cu 3Au alloys aged at 523 and 653 K that were obtained by averaging long-range order parameters determined for several diffraction areas with the developed method are close to the reported data obtained by the X-ray diffraction method. The main causes for the deviation of long-range order parameters determined for several diffraction areas are also discussed.

Quantitative intensity measurement of equal thickness fringes in Si and MgO crystal images with an energy-filtering transmission electron microscope using an imaging plate.

Quantitative measurement of intensity profiles of equal thickness fringes has been carried out in Si and MgO crystal images with an energy-filtering transmission electron microscope using an imaging plate. The crystals have a 90 degrees wedge-shape with [110] surfaces for Si and with [100] surfaces for MgO, and are observed under the exact axial incidence of a 200 keV electron beam along the [100] axis for Si and along the [110] axis for MgO. The intensities are measured in bright field and 022 and 040 dark field images for Si, and in bright field and 111, 002, 220, 113, 222, and 004 dark field images for MgO, with and without an energy slit having +/- 5 eV energy width for incident electrons. The intensity profiles obtained from the images are presented as standard experimental data for calculation of electron diffraction intensities. A few simulation programs for high-resolution transmission electron microscopy are checked by comparing the calculated diffraction intensities with the experimental data. The complex potential suitable for matching the data is discussed.

Models for termination of crystal boundaries in the theory of transmission electron diffraction and comparison with experimental data

Calculations of electron diffraction intensities in transmission electron microscopy commonly assume a model representing surfaces and interfaces in crystals as flat boundaries (flat-boundary model, FBM). It is shown that the independent-atom model (IAM) representing the crystal potential as a superposition of spherical atomic potentials leads to improved boundary conditions. Intensities calculated from the two models at large deviation from the Bragg peak in weak reflections (e.g. 200 in InGaAs) differ significantly. Results from both types of calculation are compared with an experimental diffraction pattern recorded using energy-filtered largeangle convergent-beam electron diffraction from an In 0.53 Ga 0.47 /InP bicrystal. It is shown that calculations using the IAM give a better agreement with experiment

The calculation of electron diffraction intensities by the multislice method

The calculation of wave functions of scattered electrons by the multislice method of Cowley and Moodie with a finite number of beams is shown to lead to the solution of a finite, closed set of differential equations in the limit that the slice thickness approaches zero. The solution is normalized but differs from the exact wave function unless sufficient beams are included in the calculation. Hence, normalization is not sufficient to ensure that the computed wave function equals the exact wave function. The implications of this result for numerical work are discussed.

On the calculation of electron diffraction intensities

It is pointed out that the 'discrepancy' between the electron diffraction intensities calculated by Sturkey (1962) and by Fukuhara (1966) is not due to any inherent inaccuracy of Sturkey's method of calculation, and that the correct explanation of the discrepancy is that Sturkey's calculations refer to positron diffraction while those of Fukuhara refer to electron diffraction. A corrected form of Sturkey's development of the theory is given.