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.

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.

Quantitative Convergent Beam Electron Diffraction Measurements of Low-Order Structure Factors in Copper

2003 ◽  
Vol 9 (5) ◽  
pp. 379-389 ◽  
Author(s):  
Jesper Friis ◽  
Bin Jiang ◽  
John C.H. Spence ◽  
Randi Holmestad
Keyword(s):  
Electron Diffraction ◽  
High Energy ◽  
Convergent Beam Electron Diffraction ◽  
Order Structure ◽  
Band Theory ◽  
Beam Electron ◽  
Structure Factors ◽  
A Charge ◽  
Convergent Beam ◽  
Low Order

Accurate low-order structure factors for copper metal have been measured by quantitative convergent beam electron diffraction (QCBED). The standard deviation of the measured structure factors is equal to or smaller than the most accurate measurement by any other method, including X-ray single crystal Pendellösung, Bragg γ-ray diffraction, and high-energy electron diffraction. The electron structure factor for the (440) reflection was used to determine the Debye-Waller (DW) factor. The local heating of the specimen by the electron beam is determined to be 5 K under the current illumination conditions. The low-order structure factors for copper measured by different methods are compared and discussed. The new data set is used to test band theory and to obtain a charge density map. The charge deformation map shows a charge surplus between the atoms and agrees fairly well with the simple model of copper 2+ ions at the atomic sites in a sea of free uniformly distributed electrons.

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.

Improvement of precision in refinements of structure factors using convergent-beam electron diffraction patterns taken at Bragg-excited conditions

2021 ◽  
Vol 77 (4) ◽  
Author(s):  
B. Aryal ◽  
D. Morikawa ◽  
K. Tsuda ◽  
M. Terauchi
Keyword(s):  
Electron Diffraction ◽  
Reciprocal Lattice ◽  
Correlation Coefficients ◽  
Atomic Displacement ◽  
Convergent Beam Electron Diffraction ◽  
Order Structure ◽  
Beam Electron ◽  
Structure Factors ◽  
Atomic Displacement Parameters ◽  
Convergent Beam

A local structure analysis method based on convergent-beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low-order structure factors with sin θ/λ ≤ 0.28 Å−1 of potassium tantalate (KTaO3). Comparison between structure factors determined from CBED patterns taken at the zone-axis (ZA) and Bragg-excited conditions is made in order to discuss their precision and sensitivities. Bragg-excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg-excited CBED patterns has been found only for structure factors of the outer zeroth-order Laue-zone reflections with larger reciprocal-lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg-excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors.

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.

Quantitative Zone-Axis Convergent Beam Electron Diffraction: Current Status and Future Prospects

2003 ◽  
Vol 9 (5) ◽  
pp. 411-418 ◽  
Author(s):  
Martin Saunders
Keyword(s):  
Electron Diffraction ◽  
Charge Density ◽  
Convergent Beam Electron Diffraction ◽  
Zone Axis ◽  
Current Status ◽  
Crystalline Materials ◽  
Beam Electron ◽  
Structure Factors ◽  
Bond Charge ◽  
Convergent Beam

Quantitative zone-axis convergent beam electron diffraction (CBED) is now an established technique. Over the past decade it has been developed into a tested method for the accurate refinement of structure factors, allowing the details of the charge density and bonding effects to be studied in crystalline materials. Strategies for obtaining the most accurate results have evolved, and the most important influences on the accuracy have been determined. Initial applications of the technique to bond charge density determination have led to the extension of the method to the refinement of other important parameters influencing the experimental data, such as Debye–Waller factors and the absorption potential. The development and current status of quantitative zone-axis CBED are discussed. Prospects for the future development and application of the technique are also considered.

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.

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