scholarly journals Accurate Structure Factor Measurements by Powder Methods

1988 ◽  
Vol 41 (3) ◽  
pp. 413 ◽  
Author(s):  
TM Sabine
Keyword(s):  
Structure Factor ◽  
Waller Factor ◽  
Physical Situation ◽  
Thermal Diffuse Scattering ◽  
Debye Waller Factor ◽  
Structure Factors ◽  
Kinematic Approximation ◽  
Kinematic Behaviour ◽  
Different Grain Size ◽  
Thermal Diffuse

Powder diffraction data are normally analysed by Rietveld refinement. In this technique the observed diffraction. pattern is fitted to a calculated pattern by least-squares methods. The accuracy with which structure factors can be determined is dependent on the parameters in the model being an accurate representation of the physical situation. The Rietveld model is derived in the kinematic approximation. Deviations from kinematic behaviour because of extinction, absorption, thermal diffuse scattering, and multiple scattering are then included in the model. As a test of the method the Debye-Waller factor (which is the only unknown component of the structure factor) is determined for magnesium oxide from time-of-Bight neutron data on four specimens of very different grain size.

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

2010 ◽  
Vol 16 (S2) ◽  
pp. 938-939 ◽  
Author(s):  
X Sang ◽  
A Kulovits ◽  
JMK Wiezorek
Keyword(s):  
Electron Diffraction ◽  
Structure Factor ◽  
Waller Factor ◽  
Convergent Beam Electron Diffraction ◽  
Beam Electron ◽  
Debye Waller Factor ◽  
Fitting Method ◽  
Method Optimization ◽  
Convergent Beam

Extended abstract of a paper presented at Microscopy and Microanalysis 2010 in Portland, Oregon, USA, August 1 – August 5, 2010.

Experimental measurement of Debye-Waller factors

1995 ◽  
Vol 53 ◽  
pp. 138-139
Author(s):  
J. M. Zuo ◽  
R. Holmestad ◽  
Y. Tomokiyo ◽  
K. Yase
Keyword(s):  
Symmetric Matrix ◽  
Theoretical Calculations ◽  
Waller Factor ◽  
High Order ◽  
Order Structure ◽  
Site Symmetry ◽  
High Order Structure ◽  
Debye Waller Factor ◽  
Structure Factors ◽  
Image Position

Effects of atomic thermal vibration in a crystal on the diffracted intensities is described by the Debye-Waller factor (DWF). In general, DWF is a 3×3 symmetric matrix with six independent elements. For isotropic atomic vibration or atoms with cubic site symmetry, a single DWF B suffices: here s=sinθb/λ. DWFs are among the refined parameters in structure analysis in x-ray or neutron diffraction. The accuracy of DWF in such measurements often depends on the quality of the crystal. In quantitative electron diffraction, accurate DWF is needed for 1) converting Fourier coefficients of potential to that of charge density, 2) comparison with theoretical calculations of static crystals, 3) estimation of high order structure factor and absorption coefficients.DWF can be determined from measured amplitude of high order structure factors where the effects of bonding is minimal and DWF largest. Fig. 1 shows a plot of logrithmitic of ratios of measured MgO electron structure factors and calculated ones without temperature factor.

Are Common Atom Form Factors in HREM-Simulations Accurate Enough for Quantitative Image Matching?

1997 ◽  
Vol 3 (S2) ◽  
pp. 1159-1160
Author(s):  
G. Möbus ◽  
T. Gemming ◽  
W. Nüchter ◽  
M. Exner ◽  
P. Gumbsch ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Image Matching ◽  
Form Factors ◽  
Waller Factor ◽  
Dynamics Simulation ◽  
Simulated Image ◽  
Thermal Diffuse Scattering ◽  
Hartree Fock ◽  
Debye Waller Factor ◽  
Quantitative Image

1.Introduction:If digital image matching between an experimental HREM-image and the simulated image fails, one of the suggested reasons is the “inaccuracy of the atomic form factors“ describing the electron scattering in common simulation packages using the free and neutral atom approximation from Hartree-Fock calculations [1]. In detail, three contributions within the usual form factor calculations are mainly missing: (i) the redistribution of charge in ionic crystals, (ii) the accumulation of charge away from atom sites in covalent crystals, (iii) the inclusion of thermal diffuse scattering (TDS) as well as the correlated vibration of atoms beyond the Einstein-approximation within the Debye-Waller factor (DWF) theory. Each of the three effects have been checked separately:2.Simulations of TDS by Coupling of Molecular Dynamics Time Series to HREM- Multislice Calculations:70 snap shots of a series of structures of NiAl (4.9 × 5.1 × l0nm) are stored from an equilibrated molecular dynamics simulation with vibration amplitudes corresponding to room temperature.

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