Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. I. Structure-factor measurements

1999 ◽  
Vol 55 (3) ◽  
pp. 471-479 ◽  
Author(s):  
M. Saunders ◽  
A. G. Fox ◽  
P. A. Midgley
Keyword(s):  
Solid State ◽  
Electron Diffraction ◽  
Structure Factor ◽  
Wave Theory ◽  
Zone Axis ◽  
Critical Voltage ◽  
Order Structure ◽  
Full Potential ◽  
Thermal Diffuse Scattering ◽  
Einstein Model

The zone-axis CBED pattern-matching technique ZAPMATCH [Bird & Saunders (1992). Ultramicroscopy, 45, 241–251] has been applied to low-order structure-factor measurements in nickel and copper. Considerable disagreement exists between previously published results obtained with a variety of solid-state theories and experimental techniques. The nickel ZAPMATCH results confirm previous electron-diffraction critical-voltage measurements and are in excellent agreement with FLAPW (full-potential linearized augmented plane-wave) theory calculations. This is further proof of the accuracy achievable with ZAPMATCH analysis. For copper, however, while the results support the findings of previous experimental measurements, they are consistently higher than those given by a range of solid-state theories, perhaps demonstrating some limitation in the existing theory. Two extensions to the ZAPMATCH technique are also considered. First, rules are developed to determine the number of structure factors that can be refined accurately from a given CBED pattern. Second, the imaginary potential generally introduced to account for the effects of thermal diffuse scattering (TDS) is also refined. It is shown that, while the widely used Einstein model is a useful approximation, the refined values are consistently higher than the model predicts. In addition, the importance of a second-order (real) TDS correction arising from the Einstein model is investigated. Although its effects are limited in this instance, it may prove to be more significant at lower beam energies or for materials of higher atomic number.

What is the ultimate precision of CBED structure factor measurement? Application to Group IV and III-V semiconductors

1995 ◽  
Vol 53 ◽  
pp. 144-145
Author(s):  
M. Saunders ◽  
P.A. Midgley ◽  
R. Vincent
Keyword(s):  
Solid State ◽  
Electron Diffraction ◽  
Charge Density ◽  
Pattern Matching ◽  
State Theory ◽  
Group Iv ◽  
Zone Axis ◽  
Order Structure ◽  
Solid State Theory ◽  
Bond Charge

We have previously demonstrated the feasibility of fitting calculated zone-axis Convergent Beam Electron Diffraction (CBED) patterns to zero-loss energy-filtered experimental data. The aim of this pattern matching procedure is to refine accurate low-order structure factors that can be used to reconstruct the bonding charge density. Initial tests on silicon [110] zone-axis patterns have shown that this new electron diffraction technique is capable of accuracies comparable with existing X-ray methods and that the results are in good agreement with solid state theory calculations. The general applicability of the CBED pattern matching technique is now investigated by studying the bond charge of two other Group IV materials, i.e. germanium and diamond, and the HI-V semiconductor GaAs.The (110) plane of the reconstructed bond charge density for each of the Group IV materials is shown in Figure 1. The agreement between these results and those predicted by solid state theory is excellent despite the use of only five independent Fourier components in the reconstruction.

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.

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.

Debye-Waller Factor Measurements by Quantitative Convergent Beam Electron Diffraction (CBED)

1997 ◽  
Vol 3 (S2) ◽  
pp. 1011-1012
Author(s):  
M. Saunders ◽  
A. G. Fox ◽  
P. A. Midgley
Keyword(s):  
Electron Diffraction ◽  
Waller Factor ◽  
Order Structure ◽  
Crystalline Materials ◽  
Thermal Diffuse Scattering ◽  
X Ray ◽  
Debye Waller Factor ◽  
Convergent Beam ◽  
Thermal Diffuse ◽  
Limited Accuracy

Quantitative CBED techniques are now capable of making low-order structure factor measure-ments with sufficient accuracy to study bonding effects in crystalline materials. The main limitation of these techniques has been identified as the accuracy with which one knows the Debye-Waller factor(s) (DWF(s)). Even where X-ray measurements exist, values have usually been determined at room temperature whereas we often want to perform our electron diffraction experiments at liquid nitrogen temperatures to reduce the effects of thermal diffuse scattering (TDS). Attempts to calculate theoretical DWF values have been shown to have limited accuracy when compared to experimental measurements.This has led to a search for new electron diffraction methods for DWF determination such as the use of HOLZ line segments, high-index systematic rows and electron precession patterns. The aim should be to measure the DWF(s) under identical conditions to those used for the charge density studies, e.g. the same sample thickness, temperature and microscope settings.

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.

scholarly journals Structure factor measurement in TiAl and silicon

1995 ◽  
Vol 53 ◽  
pp. 150-151
Author(s):  
S. Swaminathan ◽  
J. M. Wiezorek ◽  
I. P. Jones ◽  
N. J. Zaluzec ◽  
D. M. Maher ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Diffraction Theory ◽  
Bloch Wave ◽  
Order Structure ◽  
Electron Charge Density ◽  
Energy Filtering ◽  
Structure Factors ◽  
Factor Measurement ◽  
Theoretical Pattern

The accurate measurement of low order structure factors is required for the determination of the electron charge density distribution in crystals. In this work the energy-filtered convergent beam electron diffraction (CBED) rocking curve method has been used for accurate structure factor measurements. This CBED method for structure factor refinement involves matching of the experimental CBED intensities to those calculated using dynamical electron diffraction theory. The CBED experiments were conducted with a Philips EM420 Transmission Electron Microscope coupled with a custom built energy-filtering attachment enabling single electron counting. The theoretical pattern matching was performed using FORTRAN programs which were developed by Swaminathan. Initially the experimental plan involved an attempt to refine structure factors of TiAl by two dimensional Bloch wave calculations. The results of this project have been reported elsewhere. Subsequently it proved impossible to obtain results with sufficient precision for TiAl reproducibly, i.e. less than 0.1%, from samples of different thicknesses.

Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. II. Debye–Waller-factor measurements

1999 ◽  
Vol 55 (3) ◽  
pp. 480-488 ◽  
Author(s):  
M. Saunders ◽  
A. G. Fox ◽  
P. A. Midgley
Keyword(s):  
Electron Diffraction ◽  
Liquid Nitrogen ◽  
Zone Axis ◽  
Electron Diffraction Data ◽  
Order Structure ◽  
Great Success ◽  
Experimental Conditions ◽  
Data Set ◽  
Structure Factors ◽  
Low Order

Quantitative CBED techniques, such as the ZAPMATCH zone-axis pattern-matching method [Bird & Saunders (1992). Ultramicroscopy, 45, 241–251], have been applied with great success to the accurate refinement of low-order structure factors. The major limitation on the accuracy of the structure-factor measurements is uncertainty in the Debye–Waller factors describing the temperature-dependent atomic vibrations. While X-ray and neutron diffraction techniques are both capable of accurate measurements of Debye–Waller factors, the frequent use of liquid-nitrogen-cooled samples in CBED experiments means that previous measurements are rarely available at the temperatures required. This has prompted attempts to determine Debye–Waller factors from electron diffraction data obtained under experimental conditions that match those used for the quantitative CBED work. In this paper, the possibility of extracting accurate Debye–Waller factors from the low-order reflections of a zone-axis CBED pattern is investigated. In this way, the Debye–Waller factors and structure factors could be obtained from the same data set. With this new approach, it is shown that errors lower than ±0.02 Å2 can be obtained for the measurement of Debye–Waller factors from room- and liquid-nitrogen-temperature nickel and copper 〈110〉 zone-axis data. The results obtained are compared with previous measurements and theoretical predictions.

Computer Indexing of Electron Diffraction Patterns Including the Effects of Lattice Symmetry

1977 ◽  
Vol 35 ◽  
pp. 22-23
Author(s):  
J. S. Lally ◽  
R. J. Lee
Keyword(s):  
Electron Diffraction ◽  
Zone Axis ◽  
Crystal Thickness ◽  
Double Diffraction ◽  
Automated Method ◽  
Lattice Symmetry ◽  
Intensity Calculations ◽  
Unknown Structure ◽  
Diffraction Patterns ◽  
Orientation Parameters

In the 50 year period since the discovery of electron diffraction from crystals there has been much theoretical effort devoted to the calculation of diffracted intensities as a function of crystal thickness, orientation, and structure. However, in many applications of electron diffraction what is required is a simple identification of an unknown structure when some of the shape and orientation parameters required for intensity calculations are not known. In these circumstances an automated method is needed to solve diffraction patterns obtained near crystal zone axis directions that includes the effects of systematic absences of reflections due to lattice symmetry effects and additional reflections due to double diffraction processes.Two programs have been developed to enable relatively inexperienced microscopists to identify unknown crystals from diffraction patterns. Before indexing any given electron diffraction pattern, a set of possible crystal structures must be selected for comparison against the unknown.

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