Determination of structure factors in electron diffraction: A bloch wave picture

1985 ◽  
Vol 17 (2) ◽  
pp. 171
Author(s):  
Jon Gj∅nnes
Keyword(s):  
Electron Diffraction ◽  
Bloch Wave ◽  
Structure Factors

scholarly journals Non-systematic Three-beam Effects in Dynamical Electron Diffraction and Their Use in Determination of Amplitude and Phase of Structure Factors

1988 ◽  
Vol 41 (3) ◽  
pp. 449 ◽  
Author(s):  
K Marthinsen ◽  
H Matsuhata ◽  
R Hfier ◽  
J Gjfnnes
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Bloch Wave ◽  
Critical Voltage ◽  
Dispersion Surface ◽  
Structure Factors ◽  
Three Phase ◽  
Convergent Beam ◽  
Diffraction Condition

The treatment of non-systematic multiple-beam effects in dynamical diffraction is extended. Expressions for Bloch wave degeneracies are given in the centrosymmetrical four-beam case and for some symmetrical directions. These degeneracies can be determined experimentally either as critical voltages or by locating the exact diffraction condition at a fixed voltage. The accuracy when applied to structure factor determination is comparable with the systematical critical voltage, namely 1% in UfT The three-beam case 0, g, h is treated as well in the non-centrosymmetrical case, where it can be used for determination of phases. It is shown that the contrast features can be represented .by an effective structure factor defined by the gap at the dispersion surface. From the variation in the gap with diffraction condition, a method to determine the three-phase structure invariant I\J = 9 + _ h + h _ 9 is given. The method is based upon the contrast asymmetry in the weaker diffracted beam and can be applied in Kikuchi, convergent beam or channelling patterns. Calculations relating to channelling in backscattering are also presented.

scholarly journals Determination of structure factors of copper by convergent beam electron diffraction

1993 ◽  
Vol 51 ◽  
pp. 688-689
Author(s):  
John Mansfield ◽  
Martin Saunders ◽  
George Burgess ◽  
David Bird ◽  
Nestor Zaluzec
Keyword(s):  
Electron Diffraction ◽  
National Laboratory ◽  
Pure Copper ◽  
Argonne National Laboratory ◽  
Convergent Beam Electron Diffraction ◽  
Beam Electron ◽  
Structure Factors ◽  
Convergent Beam ◽  
Ray Methods

There has been considerable recent interest in the determination of structure factors from convergent-beam electron diffraction (CBED) patterns and the ultimate goal is the ability to retrieve the crystal structure of an unknown crystal by inversion of a CBED pattern. There are a number of different methods that have been used to extract structure factor information. The zone-axis pattern fitting technique of Bird and Saunders has recently been used to obtain structure factors for silicon that compare well with those obtained by X-ray methods. This work extends the techniques to f.c.c. metals, specifically copper.CBED patterns were recorded from [110] zone axes of electropolished foils of pure copper (99.999% purity) in the Philips EM420T at Argonne National Laboratory. The patterns were energy-filtered by scanning the whole pattern across the entrance aperture of a Gatan #607 serial energy loss spectrometer and collecting the zero loss intensity only (energy window ∼5eV).

scholarly journals Structure factor measurement in TiAl and silicon

1995 ◽  
Vol 53 ◽  
pp. 150-151
Author(s):  
S. Swaminathan ◽  
J. M. Wiezorek ◽  
I. P. Jones ◽  
N. J. Zaluzec ◽  
D. M. Maher ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Diffraction Theory ◽  
Bloch Wave ◽  
Order Structure ◽  
Electron Charge Density ◽  
Energy Filtering ◽  
Structure Factors ◽  
Factor Measurement ◽  
Theoretical Pattern

The accurate measurement of low order structure factors is required for the determination of the electron charge density distribution in crystals. In this work the energy-filtered convergent beam electron diffraction (CBED) rocking curve method has been used for accurate structure factor measurements. This CBED method for structure factor refinement involves matching of the experimental CBED intensities to those calculated using dynamical electron diffraction theory. The CBED experiments were conducted with a Philips EM420 Transmission Electron Microscope coupled with a custom built energy-filtering attachment enabling single electron counting. The theoretical pattern matching was performed using FORTRAN programs which were developed by Swaminathan. Initially the experimental plan involved an attempt to refine structure factors of TiAl by two dimensional Bloch wave calculations. The results of this project have been reported elsewhere. Subsequently it proved impossible to obtain results with sufficient precision for TiAl reproducibly, i.e. less than 0.1%, from samples of different thicknesses.

Analysis by Electron Diffraction of a Rhombohedral Al-Ge Phase

1990 ◽  
Vol 48 (2) ◽  
pp. 524-525
Author(s):  
R. Vincent ◽  
D. R. Exelby
Keyword(s):  
Electron Diffraction ◽  
Large Angle ◽  
Zone Axis ◽  
Large Unit ◽  
Intensity Measurements ◽  
Local Perturbations ◽  
Structure Factors ◽  
Unit Cells ◽  
Zero Layer

Although we have shown in previous work that large angle CBED (LACBED) patterns excited around zone axes include kinematic intensities suitable for determination of unknown structures, the data collection and processing required is quite considerable, especially for crystals with moderately large unit cells. As a preliminary guide to a structure, we have investigated the utility of approximate structure factors and phases obtained from zero layer reflections excited around a major zone axis, followed by a Fourier or Patterson transform to estimate projected atom positions. Naturally, dynamical effects cannot be avoided but the use of focussed LACBED patterns implies that local perturbations from non-systematic reflections are not an important factor that limit the accuracy of intensity measurements. Furthermore, it is convenient here to separate reflections into two sets, where the majority are essentially two-beam in character, whereas the remainder lie within strong systematic rows. Even within these rows, only the extinction distances of weaker reflections are likely to be seriously perturbed, and therefore affect the accuracy of structure factors.

Some Applications of the U. S. Steel MVEM

1973 ◽  
Vol 31 ◽  
pp. 4-5
Author(s):  
J. S. Lally ◽  
L. E. Thomas ◽  
R. M. Fisher
Keyword(s):  
Electron Diffraction ◽  
Debye Temperature ◽  
Metals And Alloys ◽  
Critical Voltage ◽  
Dynamical Diffraction ◽  
Phase Structures ◽  
Structure Factors ◽  
Local Bonding ◽  
Diffraction Phenomenon ◽  
Multi Phase

A variety of materials containing many different microstructures have been examined with the USS MVEM. Three topics have been selected to illustrate some of the more recent studies of diffraction phenomena and defect, grain and multi-phase structures of metals and minerals.(1) Critical Voltage Effects in Metals and Alloys - This many-beam dynamical diffraction phenomenon, in which some Bragg resonances vanish at certain accelerating voltages, Vc, depends sensitively on the spacing of diffracting planes, Debye temperature θD and structure factors. Vc values can be measured to ± 0.5% in the HVEM ana used to obtain improved extinction distances and θD values appropriate to electron diffraction, as well as to probe local bonding effects and composition variations in alloys.

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