Kinematical structure factors from dynamical diffraction?

1993 ◽  
Vol 51 ◽  
pp. 676-677
Author(s):  
Alwyn Eades
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Multiple Diffraction ◽  
Full Account ◽  
Structure Factors ◽  
Simplified Method ◽  
Common Observation ◽  
Symmetry Relations ◽  
Convergent Beam ◽  
Beam Diffraction

In convergent-beam diffraction it is a common observation that kinematically forbidden reflections show "dynamical extinctions", also known as Gjonnes-Moodie lines, G-M lines, black crosses or dark bars. These zeros of intensity can be understood as resulting from the pairing of multiple diffraction routes so that each pair cancels. If the multiple diffraction routes for a reflection that is not kinematically forbidden could be paired in the same way, we could locate a position in the convergent-beam disc where the intensity would depend only on the structure factor for that one reflection. This would be extremely valuable because it would provide electron diffraction with a greatly simplified method of solving crystal structures.It turns out that no such condition can be found. Here, an outline of the argument is given. A full account will be given elsewhere.The pairing of the multiple diffraction routes depends on the existence of symmetry relations between different reflections.

scholarly journals Structure factor measurement by 3-beam convergent beam electron diffraction

2014 ◽  
Vol 70 (a1) ◽  
pp. C1623-C1623
Author(s):  
Yueming Guo ◽  
Philip Nakashima ◽  
Joanne Etheridge
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Convergent Beam Electron Diffraction ◽  
Beam Electron ◽  
Direct Observations ◽  
Structure Factors ◽  
Factor Measurement ◽  
Relative Structure ◽  
Convergent Beam ◽  
Approximate Measurement

It has been shown mathematically that both the magnitudes and 3-phase invariants of the structure factors of a centrosymmetric crystal can be expressed explicitly in terms of the distances to specific features in the 3-beam convergent beam electron diffraction (CBED) pattern [1].This theoretical inversion can be implemented experimentally, enabling direct observations of 3-phase invariants and the approximate measurement of structure factor magnitudes. This method then enables a different approach to crystal structure determination, which is based on the observation of phases, rather than the measurement of amplitudes. It has been shown that by inspection of just a few phases using 3-beam CBED patterns, centrosymmetric crystal structures can be determined directly to picometre precision without the need to measure magnitudes [2]. Here, we will explore a different approach for measuring structure factor magnitudes from 3-beam CBED patterns. It has been demonstrated that the relative structure factor magnitudes can be determined directly from the ratio of the intensity distributions along specific lines within the CBED discs [3]. We will investigate the potential of using this approach for the relatively fast measurement of approximate structure factor magnitudes from nano-scale volumes of crystals.

scholarly journals On the experimental determination of low-order structure factors in TiAl by energy-filtered convergent-beam electron diffraction

1993 ◽  
Vol 51 ◽  
pp. 662-663
Author(s):  
S. Swaminathan ◽  
I. P. Jones ◽  
N. J. Zaluzec ◽  
D. M. Maher ◽  
H. L. Fraser
Keyword(s):  
Electron Diffraction ◽  
Charge Density ◽  
Structure Factor ◽  
Convergent Beam Electron Diffraction ◽  
Order Structure ◽  
Electron Charge Density ◽  
Beam Electron ◽  
Structure Factors ◽  
Convergent Beam ◽  
Low Order

It has been claimed that the effective Peierls stresses and mobilities of certain dislocations in TiAl are influenced by the anisotropy of bonding charge densities. This claim is based on the angular variation of electron charge density calculated by theory. It is important to verify the results of these calculations experimentally, and the present paper describes a series of such experiments. A description of the bonding charge density distribution in materials can be obtained by utilizing the charge deformation density (Δρ (r)) defined by(1) where V is the volume of the unit cell, Fobs is the experimentally determined low order structure factor and Fcalc is the structure factor calculated using the Hartree-Fock neutral atom model. To determine the experimental low order structure factors, a technique involving a combination of convergent beam electron diffraction (CBED) and electron energy loss spectroscopy (EELS) has been used.

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.

How do specimen preparation and crystal perfection affect structure factor measurements by quantitative convergent-beam electron diffraction?

2017 ◽  
Vol 50 (2) ◽  
pp. 602-611 ◽  
Author(s):  
Ding Peng ◽  
Philip N. H. Nakashima
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Convergent Beam Electron Diffraction ◽  
Specimen Preparation ◽  
Crystalline Materials ◽  
Beam Electron ◽  
Crystal Perfection ◽  
Transmission Electron ◽  
Structure Factors ◽  
Convergent Beam

The effectiveness of tripod polishing and crushing as methods of mechanically preparing transmission electron microscopy specimens of hard brittle inorganic crystalline materials is investigated via the example of cerium hexaboride (CeB6). It is shown that tripod polishing produces very large electron-transparent regions of very high crystal perfection compared to the more rapid technique of crushing, which produces crystallites with a high density of imperfections and significant mosaicity in the case studied here where the main crystallite facets are not along the natural {001} cleavage planes of CeB6. The role of specimen quality in limiting the accuracy of structure factor measurements by quantitative convergent-beam electron diffraction (QCBED) is investigated. It is found that the bonding component of structure factors refined from CBED patterns obtained from crushed and tripod-polished specimens varies very significantly. It is shown that tripod-polished specimens yield CBED patterns of much greater integrity than crushed specimens and that the mismatch error that remains in QCBED pattern matching of data from tripod-polished specimens is essentially nonsystematic in nature. This stands in contrast to QCBED using crushed specimens and lends much greater confidence to the accuracy and precision of bonding measurements by QCBED from tripod-polished specimens.

Chiral determination: direct interpretation of convergent-beam electron diffraction patterns using the series expansion of Cowley and Moodie

2007 ◽  
Vol 63 (4) ◽  
pp. 511-520 ◽  
Author(s):  
Andrew W. S. Johnson
Keyword(s):  
Electron Diffraction ◽  
Series Expansion ◽  
Convergent Beam Electron Diffraction ◽  
Chiral Structure ◽  
Beam Electron ◽  
Structure Factors ◽  
Direct Interpretation ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Diffraction

Given a small number of structure factors of a known chiral structure of unknown hand, it is shown that the hand can be determined from the sign of the contrast difference of two reflections in a suitably oriented convergent-beam electron diffraction (CBED) pattern. A simple formula for this difference, which takes into account all the significant second-order scattering, is derived using the series expansion of Cowley and Moodie for n-beam diffraction. The reason for the success of a three-beam interpretation is investigated. The method is applied to patterns from thin crystals in which a mirror projection symmetry can be found and its validity is demonstrated by agreement with experiment using samples of known hand. The advantages of recording patterns near major zone axes are discussed as well as some other experimental aspects of chiral determination using CBED.

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.

Crystal Polarity Determination by Electron Channeling

2001 ◽  
Vol 7 (S2) ◽  
pp. 334-335
Author(s):  
J. Tafto
Keyword(s):  
Experimental Conditions ◽  
Electron Channeling ◽  
Structure Factors ◽  
Small Crystals ◽  
Polarity Determination ◽  
Convergent Beam ◽  
Interface Structures ◽  
Diffraction Effects ◽  
Beam Diffraction

Multilayers, heterostructures, nanostructures and composites are of great interest to the materials scientists, and frequently we encounter crystals lacking centrosymmetry. Thus crystal polarity determination on a microscopic scale is becoming increasingly important in describing interface structures and the internal defects in small crystals. in many cases the polarity of a crystallite can be determined by convergent beam electron diffraction, CBED. Powerful alternatives are to monitor the electron induced x-ray emission, EDS, or electron energy losses, EELS, under channeling conditions. While the determination of the phase of the structure factors, and thus the determination of the crystal polarity, relies on many beam diffraction effects when the CBED technique is used, two-beam experiments provide information about the phase of the structure factor when localized EDS or EELS signals are detected under channeling conditions.The experimental conditions used to determine the polarity and absolute orientation from electron channeling are similar to those used in ALCHEMI experiments to locate small amounts of atoms by electron channeling.

The role of projection operators in the theory of N-beam diffraction and the inversion of three-beam elastic scattering intensities

1999 ◽  
Vol 55 (2) ◽  
pp. 216-219 ◽  
Author(s):  
A. C. Hurley ◽  
A. F. Moodie ◽  
A. W. S. Johnson ◽  
P. C. Abbott
Keyword(s):  
Elastic Scattering ◽  
Electron Diffraction ◽  
Electron Diffraction Pattern ◽  
Convergent Beam Electron Diffraction ◽  
Projection Operators ◽  
Mathematical Basis ◽  
Beam Electron ◽  
Convergent Beam ◽  
Beam Diffraction

Commencing from a projection-operator description of N-beam diffraction, the mathematical basis for the recovery of phase and amplitude information from a three-beam convergent-beam electron diffraction pattern is given for both the centrosymmetric and noncentrosymmetric cases. The algebra is available in Mathematica Notebook form from the URL ftp://ftp.physics.uwa.edu.au/pub/EMC/3BeamAlgebra.nb.

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