Quantitative Convergent Beam Electron Diffraction for Simultaneous Structure Factor and Debye Waller Factor Determination - Fitting Method Optimization

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.

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

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100149143 ◽

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.

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Low-Order Structure-Factor Amplitude and Sign Determination of an Unknown Structure AlmFe by Quantitative Convergent-Beam Electron Diffraction

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767396008379 ◽

1996 ◽

Vol 52 (6) ◽

pp. 923-936 ◽

Cited By ~ 11

Author(s):

Y. F. Cheng ◽

W. Nüchter ◽

J. Mayer ◽

A. Weickenmeier ◽

J. Gjønnes

Keyword(s):

Electron Diffraction ◽

Structure Factor ◽

Convergent Beam Electron Diffraction ◽

Order Structure ◽

Beam Electron ◽

Unknown Structure ◽

Convergent Beam ◽

Sign Determination ◽

Low Order

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

Journal of Applied Crystallography ◽

10.1107/s1600576717003260 ◽

2017 ◽

Vol 50 (2) ◽

pp. 602-611 ◽

Cited By ~ 3

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.

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