On the accuracy of structure-factor measurements in GaAs by CBED

1988 ◽  
Vol 46 ◽  
pp. 824-825
Author(s):  
J.M. Zuo ◽  
M. O'Keeffe ◽  
J.C.H. Spence
Keyword(s):  
Structure Factor ◽  
Phonon Scattering ◽  
Three Dimensional ◽  
Bloch Wave ◽  
Bragg Angle ◽  
Order Structure ◽  
Structure Factors ◽  
Convergent Beam ◽  
Electron Energy Loss ◽  
Low Order

By comparing the experimental intensity in convergent-beam electron diffraction (CBED) patterns along the [h,0,0], [h,h,0] and [h,h,h] systematics directions with three-dimensional Bloch-wave calculations, we have refined the low-order structure factor amplitudes of GaAs. (For Si, see) The experimental data were collected using a Philips EM400 electron microscope and a Gatan model 607 electron energy loss spectrometer (EELS) tuned to the elastic peak. By placing the scan coils of the microscope under the control of a PDP11 computer, the CBED patterns could be scanned over the EELS entrance slit. Data were collected at 120kV and -183°C to reduce phonon scattering and contamination. The angular resolution was 0.6% of the (200) Bragg angle. The refinement parameters in the calculations were high voltage (obtained from HOLZ lines), thickness (obtained from outer CBED fringes), absorption potentials (from the asymmetry of the (000) disk) and the low-order structure factors Vg (from inner peaks).

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.

On the accurate measurement of low-order structure factor amplitudes and phases by quantitative CBED

1989 ◽  
Vol 47 ◽  
pp. 494-495
Author(s):  
J.C.H. Spence ◽  
J.M. Zuo
Keyword(s):  
Theoretical Calculations ◽  
Computer Control ◽  
Three Dimensional ◽  
Bloch Wave ◽  
Order Structure ◽  
Ionic Character ◽  
Structure Factors ◽  
Mott Formula ◽  
A Charge ◽  
Low Order

Over the past four years we have developed the software and computer control of electron microscope data acquisition needed for quantitative electron crystallography. CBED patterns in the systematics orientation (see Fig. 1) are scanned over the slit of a Gatan Model 607 ELS unit, and the energy filtered elastic scattering rocking curves compared with the results of theoretical calculations (see Figs. 2 and 3). The calculations are based on the Bloch wave method, and treat three-dimensional dynamical diffraction from a non-centrosymmetric crystal with absorption and inclined boundary conditions. The Fortran source code has been published, and is available by Bitnet from ZALUZEC @ANLMST. High voltage, sample thickness, absorption coefficients Vg and selected low order structure factors Vg are adjusted(using the most sensitive portion of the pattern for each)for best fit. The resulting Fourier coefficients of crystal potential may be used (via the Mott Formula) to obtain a charge density difference map, which reveals the distribution of valence electrons involved in bonding, as shown for GaAs in figure 4.The partially ionic character of the bond is seen. We find V(111)1/V(111) = 0.05, V1 (220)/V(220) = 0.035, V1 (400)/V (400) = 0.07 and V1 (333)/V(333)=0.08. Results for work on MgO in progress are shown in figs. 2 and 3.

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.

Quantitative Convergent Beam Electron Diffraction (CBED) Measurements of Low-Order Structure Factors in Nickel

1997 ◽  
Vol 3 (S2) ◽  
pp. 1013-1014
Author(s):  
M. Saunders ◽  
A. G. Fox ◽  
P. A. Midgley
Keyword(s):  
Experimental Studies ◽  
Zone Axis ◽  
Order Structure ◽  
Data Set ◽  
Crystalline Materials ◽  
Charge Densities ◽  
Structure Factors ◽  
Convergent Beam ◽  
Best Fit ◽  
Low Order

The introduction of quantitative CBED techniques in recent years has led to experimental studies of charge densities in crystalline materials with unprecedented accuracy. Despite these successes, the development process is still on-going with the aim of gaining a better understanding of the techniques. With this in mind, we have undertaken a systematic study of the low-order structure factors of nickel using the ZAPMATCH zone-axis pattern matching technique of Bird and Saunders. In this approach, a set of low-order structure factors (both elastic and absorptive components) is adjusted until a best-fit is obtained between a many-beam simulation and an elastic filtered zone-axis pattern. Additional higher-order structure factors are included to converge the scattering potential but are kept fixed at neutral atom values during the fit. The questions we set out to address are (i) how to choose the correct number of structure factors to refine from a given data-set, (ii) are the absorptive structure factor components we refine of any use, and (iii) can we determine Debye-Waller factors at the same time as we measure the charge density? The first two points are discussed here.

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.

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.

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.

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