Measurement of small structure factors by the critical-voltage effect in HEED: The superlattice reflections in β'nial, β'CoAl and γtial

1992 ◽  
Vol 50 (2) ◽  
pp. 1174-1175
Author(s):  
Alan G. Fox ◽  
Mark A. Tabbernor
Keyword(s):  
Structure Factor ◽  
High Energy ◽  
Critical Voltage ◽  
Intermetallic Alloys ◽  
Rocking Curve ◽  
X Ray ◽  
Structure Factors ◽  
Factor Measurement ◽  
Small Structure ◽  
Convergent Beam

The systematic critical voltage effect, Vc, in high energy electron diffraction has been used for some time to accurately measure low-angle x-ray structure factor structure factor amplitudes (see e.g. 1). It has a significant advantage over other methods for accurate structure factor measurement, such as systematic convergent beam rocking curve or x-ray Pendellösung techniques, in that it is capable of measuring very small structure factors such as the 222 ‘forbidden’ reflections in Si and Ge (see e.g. 2). In the present work the potential of the systematic Vc method for measuring small structure factor amplitudes and average Debye-Waller factors in the intermetallic alloys NiAl, CoAl and TiAl will be demonstrated.The structure factors, F, for ordered stoichiometric B2 alloys comprising A and B atoms such as Ni (Co)Al are given by

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).

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 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.

Improved quantitative CBED structure-factor measurement by refinement of nonlinear geometric distortion corrections

2005 ◽  
Vol 38 (2) ◽  
pp. 374-376 ◽  
Author(s):  
Philip N. H. Nakashima
Keyword(s):  
Structure Factor ◽  
Density Functional ◽  
Geometric Distortion ◽  
Experimental Uncertainty ◽  
Functional Theory ◽  
Hartree Fock ◽  
Structure Factors ◽  
Factor Measurement ◽  
Convergent Beam ◽  
Nonlinear Geometric

A new method that accounts for small but significant geometric distortions in quantitative convergent beam electron diffraction (QCBED) is briefly introduced. A summary of preliminary results obtained with this method shows an average three- to fourfold improvement in structure-factor measurement precision by QCBED. In the present work this method is applied to α-\rm Al_{2}O_{3}, a benchmark compound for charge density studies. Experimental uncertainty is reduced to a level three times smaller than differences between density functional theory and periodic Hartree–Fock calculated structure factors.

Comparative study of X-ray charge-density data on CoSb3

2013 ◽  
Vol 69 (6) ◽  
pp. 570-582 ◽  
Author(s):  
Mette Stokkebro Schmøkel ◽  
Lasse Bjerg ◽  
Finn Krebs Larsen ◽  
Jacob Overgaard ◽  
Simone Cenedese ◽  
...  
Keyword(s):  
Charge Density ◽  
High Performance ◽  
Theoretical Data ◽  
High Energy ◽  
Data Sets ◽  
High Symmetry ◽  
X Ray ◽  
Structure Factors ◽  
Small Crystals ◽  
Density Analysis

CoSb3is an example of a highly challenging case for experimental charge-density analysis due to the heavy elements (suitability factor of ∼0.01), the perfect crystallinity and the high symmetry of the compound. It is part of a family of host–guest structures that are potential candidates for use as high-performance thermoelectric materials. Obtaining and analysing accurate charge densities of the undoped host structure potentially can improve the understanding of the thermoelectric properties of this family of materials. In a previous study, analysis of the electron density gave a picture of covalent Co–Sb and Sb–Sb interactions together with relatively low atomic charges based on state-of-the-art experimental and theoretical data. In the current study, several experimental X-ray diffraction data sets collected on the empty CoSb3framework are compared in order to probe the experimental requirements for obtaining data of high enough quality for charge-density analysis even in the case of very unsuitable crystals. Furthermore, the quality of the experimental structure factors is tested by comparison with theoretical structure factors obtained from periodic DFT calculations. The results clearly show that, in the current study, the data collected on high-intensity, high-energy synchrotron sources and very small crystals are superior to data collected at conventional sources, and in fact necessary for a meaningful charge-density study, primarily due to greatly diminished effects of extinction and absorption which are difficult to correct for with sufficient accuracy.

X-Ray Investigations on Molten Cu-Sb Alloys

1994 ◽  
Vol 49 (4-5) ◽  
pp. 530-534 ◽  
Author(s):  
Th. Halm ◽  
H. Neumann ◽  
W. Hoyer
Keyword(s):  
Electronic Properties ◽  
Structure Factor ◽  
Correlation Functions ◽  
Pair Correlation ◽  
Model Structure ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structure Factors ◽  
Diffraction Structure ◽  
Eutectic Concentration

Abstract Using X-ray diffraction, structure factors and pair correlation functions of several molten Cu-Sb alloys and pure antimony were determined and compared with published structural, thermodynamic and electronic properties. The eutectic concentration Cu37Sb63 was investigated in dependence on temperature, and a model structure factor was calculated applying a segregation model.

Obtaining the structure factors for an epitaxial film using Cu X-ray radiation

2013 ◽  
Vol 46 (6) ◽  
pp. 1749-1754 ◽  
Author(s):  
P. Wadley ◽  
A. Crespi ◽  
J. Gázquez ◽  
M.A. Roldán ◽  
P. García ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Thin Films ◽  
Structure Factor ◽  
Tetragonal Symmetry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Structure Factors ◽  
Scanning Transmission

Determining atomic positions in thin films by X-ray diffraction is, at present, a task reserved for synchrotron facilities. Here an experimental method is presented which enables the determination of the structure factor amplitudes of thin films using laboratory-based equipment (Cu Kα radiation). This method was tested using an epitaxial 130 nm film of CuMnAs grown on top of a GaAs substrate, which unlike the orthorhombic bulk phase forms a crystal structure with tetragonal symmetry. From the set of structure factor moduli obtained by applying this method, the solution and refinement of the crystal structure of the film has been possible. The results are supported by consistent high-resolution scanning transmission electron microscopy and stoichiometry analyses.

Structure of Zr-Cu and Zr-Ni Liquid Alloys Studied by High-Energy X-Ray Diffraction

2007 ◽  
Vol 561-565 ◽  
pp. 1349-1352 ◽  
Author(s):  
Akitoshi Mizuno ◽  
T. Kaneko ◽  
Seiichi Matsumura ◽  
Masahito Watanabe ◽  
Shinji Kohara ◽  
...  
Keyword(s):  
Liquid Structure ◽  
High Energy ◽  
Glass Forming Ability ◽  
Liquid Alloys ◽  
X Ray Diffraction ◽  
X Ray ◽  
Glass Forming ◽  
Structure Factors ◽  
Asymmetric Shape ◽  
Second Peak

In order to obtain an insight into the high glass-forming ability of bulk metallic glasses, we have analyzed liquid structures of the Zr-Cu and the Zr-Ni binary alloys with different compositions. High-energy (E = 113 keV) x-ray diffraction experiments were carried out for the liquid alloys levitated by a conical nozzle levitation (CNL) technique. While a peculiar shoulder on the second peak was observed in the structure factors of the Zr-Cu liquid alloys, those of the Zr70Ni30 and the Zr50Ni50 liquids exhibit an asymmetric shape of the second peak. In addition, it was found that the effect of concentration variation in the liquid Zr-Ni alloys was significantly different from that of the liquid Zr-Cu alloys. The liquid structure analyses using the reverse Monte Carlo (RMC) simulation have clarified that a degree of the short-range correlation between the constituents in the liquids affects substantially the glass-forming ability of the binary Zr alloys.

Accurate charge densities from powder X-ray diffraction – a new version of the Aarhus vacuum imaging-plate diffractometer

2017 ◽  
Vol 73 (4) ◽  
pp. 521-530 ◽  
Author(s):  
Kasper Tolborg ◽  
Mads R. V. Jørgensen ◽  
Sebastian Christensen ◽  
Hidetaka Kasai ◽  
Jacob Becker ◽  
...  
Keyword(s):  
Electron Density ◽  
High Energy ◽  
Imaging Plate ◽  
High Symmetry ◽  
X Rays ◽  
X Ray Diffraction ◽  
Core Electron ◽  
X Ray ◽  
Peak Broadening ◽  
Structure Factors

In recent years powder X-ray diffraction has proven to be a valuable alternative to single-crystal X-ray diffraction for determining electron-density distributions in high-symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high-energy X-rays at a synchrotron-radiation facility. Here we present a new version of our custom-built in-vacuum powder diffractometer with the sample-to-detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal-to-background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole–Rietveld procedure and compared withab initiocalculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations.

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