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.

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.

Understanding crystal bonding: The contribution of electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 416-417
Author(s):  
Alan G. Fox ◽  
Mark A. Tabbenor ◽  
and Robert M. Fisher
Keyword(s):  
Electron Diffraction ◽  
Gamma Ray ◽  
Critical Voltage ◽  
Rocking Curve ◽  
X Ray ◽  
Band Structure Calculations ◽  
Structure Factors ◽  
Curve Method ◽  
Convergent Beam ◽  
Structure Calculations

Some of the most incisive information about bonding mechanisms in materials can be obtained from accurate X-ray crystal structure factors and Debye-Waller factors. This has long been known by diffraction workers in all fields, and in the last twenty years intensive efforts have been made to accurately measure structure factors by a variety of means. At the same time theoreticians have made progressively more sophisticated band structure calculations of structure factors (usually of cubic elements). Three experimental methods have emerged as being able to determine structure factors with the required accuracy for crystal bonding studies:- these are (i) X-ray Pendellosung methods (see e.g. 1 and 2) (ii) Gamma-ray diffraction (see e.g. 3) and various electron diffraction techniques (see e.g. 4 to 6). The best accuracy possible with all three methods is around 0.1%.The potential of electron diffraction for the accurate measurement of low-angle structure factors was first recognised in the late sixties by Goodman and Lehmfuhl (convergent beam-rocking curve method), Gjonnes and Hoier (intersecting Kikuchi line, IKL, method) and Nagata and Fukuhara (critical voltage, Vc, technique).

Bonding charge densities of Al and Cu determined by electron diffraction

1989 ◽  
Vol 47 ◽  
pp. 492-493
Author(s):  
A.G. Fox ◽  
M.A. Tabbernor ◽  
R.M. Fisher
Keyword(s):  
Electron Diffraction ◽  
Form Factors ◽  
Critical Voltage ◽  
X Ray Diffraction ◽  
Small Magnitude ◽  
X Ray ◽  
Charge Densities ◽  
Density Maps ◽  
Structure Factors ◽  
Atomic Scattering

As discussed by Zuo et al, the small magnitude of the energy which determines a crystal's structure has long provided a severe challenge for both theoreticians and experimentalists who have attempted to accurately calculate and measure the crystal structure factors of many materials. In particular the f.c.c. elements copper and aluminum have received considerable attention both theoretically and experimentally, where attempts have been made to accurately measure the atomic scattering (form) factors by a variety of means other than the traditionally inaccurate X-ray diffraction methods. Smart and Humphreys recognized that the accuracy of the low-angle form factors of Cu and Al determined by the critical voltage effect (Vc) in electron diffraction should be good enough to give bonding information about these two elements. Unfortunately, they failed to analyze the problem of the higher angle form factors correctly, and thus produced erroneous deformation charge density maps.

Structure factor determination from critical voltages in electron diffraction

1989 ◽  
Vol 47 ◽  
pp. 490-491
Author(s):  
J. Gjønnes ◽  
H. Matsuhata ◽  
J. Taftø
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Critical Voltage ◽  
Order Structure ◽  
Kikuchi Pattern ◽  
Additional Information ◽  
Selection Of Configurations ◽  
Structure Factors ◽  
Temperature Factors ◽  
Selection Of

The principle of the critical voltage method in electron diffraction is an attractive one: a relation between structure factors can be determined with high precision from measurement of the condition for vanishing contrast of a contrast detail in the Kikuchi pattern or in the CBED pattern. In practice the method meets with some apparent and real limitations. The original, second order critical voltage in the systematic case (Watanabe, Uyeda and Fukuhara) depends on high accelerating voltage and can be applied mainly to strong low order structure factors from simple substances. Accurate additional information about other structure factors and temperature factors must be obtained from other methods. In order to increase the utility of the method a wider selection of configurations suitable for measurement has to be found. Several investigators have focussed on non-systematic cases: Gjønnes and Høier, Steeds.

Isomorphous replacement in electron diffraction of wet crystals of rat hemoglobin

1983 ◽  
Vol 41 ◽  
pp. 446-447
Author(s):  
William F. Tivol ◽  
Murray Vernon King ◽  
D. F. Parsons
Keyword(s):  
Electron Diffraction ◽  
Heavy Atom ◽  
Isomorphous Substitution ◽  
X Ray Diffraction ◽  
Salt Solutions ◽  
X Ray ◽  
Isomorphous Replacement ◽  
Structure Factors ◽  
Diffraction Structure ◽  
The Mean

Feasibility of isomorphous substitution in electron diffraction is supported by a calculation of the mean alteration of the electron-diffraction structure factors for hemoglobin crystals caused by substituting two mercury atoms per molecule, following Green, Ingram & Perutz, but with allowance for the proportionality of f to Z3/4 for electron diffraction. This yields a mean net change in F of 12.5%, as contrasted with 22.8% for x-ray diffraction.Use of the hydration chamber in electron diffraction opens prospects for examining many proteins that yield only very thin crystals not suitable for x-ray diffraction. Examination in the wet state avoids treatments that could cause translocation of the heavy-atom labels or distortion of the crystal. Combined with low-fluence techniques, it enables study of the protein in a state as close to native as possible.We have undertaken a study of crystals of rat hemoglobin by electron diffraction in the wet state. Rat hemoglobin offers a certain advantage for hydration-chamber work over other hemoglobins in that it can be crystallized from distilled water instead of salt solutions.

scholarly journals A complicated quasicrystal approximant ∊16 predicted by the strong-reflections approach

2010 ◽  
Vol 66 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Mingrun Li ◽  
Junliang Sun ◽  
Peter Oleynikov ◽  
Sven Hovmöller ◽  
Xiaodong Zou ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Unit Cell ◽  
Space Groups ◽  
Inverse Fourier Transformation ◽  
Transmission Electron ◽  
Structure Factors ◽  
Precession Electron Diffraction ◽  
Density Map ◽  
Electron Density Map ◽  
Good Agreement

The structure of a complicated quasicrystal approximant ∊16 was predicted from a known and related quasicrystal approximant ∊6 by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of ∊16 were deduced from those of the known ∊6 structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ∊16. An electron-density map of ∊16 was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ∊6, the predicted structure of ∊16 contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ∊16 is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ∊16 with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.

Three-phase structure invariants and structure factors determined with the quantitative convergent-beam electron diffraction method

1999 ◽  
Vol 55 (2) ◽  
pp. 188-196 ◽  
Author(s):  
R. Høier ◽  
C. R. Birkeland ◽  
R. Holmestad ◽  
K Marthinsen
Keyword(s):  
Electron Diffraction ◽  
Phase Structure ◽  
Diffraction Method ◽  
Convergent Beam Electron Diffraction ◽  
Beam Electron ◽  
Structure Factors ◽  
Refinement Method ◽  
Three Phase ◽  
Phase Sensitive ◽  
Convergent Beam

Quantitative convergent-beam electron diffraction is used to determine structure factors and three-phase structure invariants. The refinements are based on centre-disc intensities only. An algorithm for parameter-sensitive pixel sampling of experimental intensities is implemented in the refinement procedure to increase sensitivity and computer speed. Typical three-beam effects are illustrated for the centrosymmetric case. The modified refinement method is applied to determine amplitudes and three-phase structure invariants in noncentrosymmetric InP. The accuracy of the results is shown to depend on the choice of the initial parameters in the refinement. Even unrealistic starting assumptions and incorrect temperature factor lead to stable results for the structure invariant. The examples show that the accuracy varies from 1 to 10° in the electron three-phase invariants determined and from 0.5 to 5% for the amplitudes. Individual phases could not be determined in the present case owing to spatial intensity correlations between phase-sensitive pixels. However, for the three-phase structure invariant, stable solutions were found.

Experimental Studies of Bonding Related Properties in Binary Intermetallics by Convergent Beam Electron Diffraction

2011 ◽  
Vol 1295 ◽  
Author(s):  
X. H. Sang ◽  
A. Kulovits ◽  
J. Wiezorek
Keyword(s):  
Electron Diffraction ◽  
Experimental Studies ◽  
Convergent Beam Electron Diffraction ◽  
Zone Axis ◽  
Order Structure ◽  
Electron Charge Density ◽  
Beam Electron ◽  
Structure Factors ◽  
Different Temperatures ◽  
Convergent Beam

ABSTRACTAccurate Debye-Waller (DW) factors of chemically ordered β-NiAl (B2, cP2, ${\rm{Pm}}\bar 3 {\rm{m}}$) have been measured at different temperatures using an off-zone axis multi-beam convergent beam electron diffraction (CBED) method. We determined a cross over temperature below which the DW factor of Ni becomes smaller than that of Al of ~90K. Additionally, we measured for the first time DW factors and structure factors of chemically ordered γ1-FePd (L10, tP2, P4/mmm) at 120K. We were able to simultaneously determine all four anisotropic DW factors and several low order structure factors using different special off-zone axis multi-beam convergent beam electron diffraction patterns with high precision and accuracy. An electron charge density deformation map was constructed from measured X-ray diffraction structure factors for γ1-FePd.

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