Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

Computer Prediction of Many-Beam Kikuchi Patterns

1971 ◽  
Vol 29 ◽  
pp. 174-175
Author(s):  
L. E. Thomas
Keyword(s):  
Bragg Reflection ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Critical Voltage ◽  
Image Simulation ◽  
Parallel Beam ◽  
Computer Prediction ◽  
New Developments ◽  
Diffraction Patterns ◽  
Beam Diffraction

Kikuchi diffraction patterns provide valuable information about the diffraction contrast images observed in TEM of crystals. For example, the “critical voltage” phenomenon of vanishing 2nd order Bragg reflection and the marked changes in transmission and contrast behavior above 100 kv due to increased many-beam systematic interactions are reflected in the K-patterns. New developments on a method for predicting both conventional (2-beam) and many-beam K-patterns and on CRT image simulation of the results will be discussed.Kikuchi patterns are formed by diffraction of electrons that have been diffused within the crystal by inelastic scattering from a parallel incident beam. For simplicity, however, we consider diffraction from a diffuse incident beam of appropriate angular distribution and use the reciprocity theorem of optics to relate the intensities in diffuse-beam diffraction to those in parallel beam diffraction. This allows the K-patterns to be calculated from many-beam dynamical theory of diffraction including absorption developed for TEM.

Dynamical Theory of Kikuchi Eletrons

1970 ◽  
Vol 28 ◽  
pp. 42-43
Author(s):  
T. Y. Tan
Keyword(s):  
Dynamical Behavior ◽  
Incident Beam ◽  
Beam Theory ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
Bragg Angle ◽  
Foil Thickness ◽  
Line Pair ◽  
Inelastic Electron ◽  
Kikuchi Lines

In transmission electron microscopy it is generally believed that for the pairs of Kikuchi lines resulting from inelastic scattering, the line nearer the transmitted spot on the diffraction pattern should always be associated with deficiency of electrons while the other should always contain excess electrons. However, Thomas and Bell demonstrated experimentally that in a case where the incident beam occurs at an exact Bragg angle, the intensities of the lines in a pair reversed, depending only on foil thickness. This color reversal of the Kikuchi line pair is associated with the dynamical behavior of the Kikuchi electrons where crystal absorption plays an essential role.Based on the two-beam dynamical theory for elastic electrons, a corresponding (two-beam) theory on the fine structures of the Kikuchi electron intensity distributions in relation to the various diffraction and absorption parameters has been formulated. In this theory, the Kikuchi electrons were taken to be those inelastic electrons generated in an infinitesimal thickness of the specimen which subsequently underwent Bragg diffraction. The initial inelastic electron wave amplitudes generated at any position inside the crystal were obtained phenomenologically by considering the decrease in amplitude of the elastic electrons due to absorption by the crystal.

Coupled thermal diffuse-atomic inner shell scattering in electron diffraction

1994 ◽  
Vol 52 ◽  
pp. 994-995
Author(s):  
Z. L. Wang
Keyword(s):  
Electron Diffraction ◽  
Diffuse Scattering ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Thermal Diffuse Scattering ◽  
Transmission Electron ◽  
Diffraction Patterns ◽  
Electron Energy Loss ◽  
Thermal Diffuse ◽  
Electron Energy Loss Spectra

In electron diffraction patterns, diffuse scattering at high angles is primarily generated by phonon, or thermal diffuse, scattering (TDS). Techniques were introduced to acquire the electron energy-loss spectra (EELS) of high-angle thermal-diffuse-scattered electrons (TDS-EELS) in a transmission electron microscope (TEM). With regards to the scattering mechanism, the TDS-EELS core ionization edge intensity was believed to be generated primarily by TDS - single electron, double-inelastic electron scattering processes. It was concluded from experimental data that the signal from coupled phonon - atomic inner shell excitations is stronger than that from atomic inner shell excitation alone. A formal dynamical theory is presented in this paper to illustrate the theoretical basis of the experimental observations. The theory can be applied to calculate the diffraction patterns of inelastically double-scattered electrons and the signal intensity observed in TDS-EELS.TDS is actually a statistically averaged, quasi-elastic scattering of the electrons by the crystal lattice of different thermal vibration configurations.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

NanoPDF64: software package for theoretical calculation and quantitative real-space analysis of powder diffraction data of nanocrystals

2017 ◽  
Vol 50 (6) ◽  
pp. 1821-1829 ◽  
Author(s):  
Kazimierz Skrobas ◽  
Svitlana Stelmakh ◽  
Stanislaw Gierlotka ◽  
Bogdan F. Palosz
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Analytical Formula ◽  
Real Space ◽  
Distribution Functions ◽  
Powder Diffraction Data ◽  
Space Analysis ◽  
Atomic Vibrations ◽  
Hexagonal Close Packed Structure ◽  
Diffraction Patterns

NanoPDF64is a tool designed for structural analysis of nanocrystals based on examination of powder diffraction data with application of real-space analysis. The program allows for fast building of models of nanocrystals consisting of up to several hundred thousand atoms with either cubic or hexagonal close packed structure. The nanocrystal structure may be modified by introducing stacking faults, density modulation waves (i.e.the core–shell model) and thermal atomic vibrations. The program calculates diffraction patterns and, by Fourier transform, the reduced pair distribution functionsG(r) for the models. ExperimentalG(r)s may be quantitatively analyzed by least-squares fitting with an analytical formula.

Supercooling of liquids

1952 ◽  
Vol 215 (1120) ◽  
pp. 43-46 ◽  
Keyword(s):  
Crystal Structures ◽  
Recent Change ◽  
The Other ◽  
Theoretical Interpretation ◽  
Experimental Fact ◽  
X Ray Diffraction ◽  
Diffraction Patterns ◽  
The One ◽  
The Right ◽  
Complex Crystal

I shall concentrate upon reviewing the important recent change in our appreciation of the facts of supercooling which has been brought about particularly by the work of Turnbull at the General Electric Research Laboratory in Schenectady. I suppose that most of us, talking about supercooling a couple of years ago, would have divided substances into two classes, one with simple crystal structures like gold, and all the other ‘good’ metals on the one hand, and those with complex crystal structures, such as glycerol and the silicates on the other; saying that whereas the latter class can be very much supercooled, and will form glasses, the former class can only be supercooled a very few degrees. Then we would have added that there are some ‘ bad ’ metals, with moderately complex crystal structures, such as antimony or bismuth, which can be supercooled some tens of degrees, forming an intermediate class. I think we would then have added that this is quite comprehensible. In particular, that the X-ray diffraction patterns of the monatomic liquids show us that most of the atoms have the right numbers of nearest neighbours in a first co-ordination shell, all ready in place to start the growth of a crystal; which readily explains why these substances cannot be supercooled very much—a nice simple experimental fact, with a straightforward theoretical interpretation—and both are wrong.

Kinematical two-dimensional multiple-diffraction intensity profiles. Application to ω–ψ scans of silicon and diamond obtained with synchrotron radiation

2001 ◽  
Vol 34 (2) ◽  
pp. 157-165 ◽  
Author(s):  
E. Rossmanith ◽  
A Hupe ◽  
R. Kurtz ◽  
H. Schmidt ◽  
H.-G. Krane
Keyword(s):  
Synchrotron Radiation ◽  
Incident Beam ◽  
Mosaic Structure ◽  
Two Dimensional ◽  
Diffraction Intensity ◽  
Multiple Diffraction ◽  
Crystal Sample ◽  
Diffraction Patterns ◽  
Kinematical Theory

In a previous paper by Rossmanith [J. Appl. Cryst.(2000),33, 1405–1414], expressions for the calculation of multiple-diffraction patterns observed in ω–ψ scans of Bragg reflections were derived within the framework of the kinematical theory, taking into account the divergence and wavelength spread of the incident beam, as well as the mosaic structure of the crystal sample. Agreement with CuKα experiments was demonstrated. In this paper, it is shown that the theoretical expressions are also suitable for synchrotron radiation experiments.

On the thermo-electric power of metals

1955 ◽  
Vol 228 (1175) ◽  
pp. 568-574 ◽  
Keyword(s):  
Electric Power ◽  
Alkali Metals ◽  
Phonon Scattering ◽  
Opposite Sign ◽  
Order Effects ◽  
Lattice Distribution ◽  
Thermo Electric ◽  
The One ◽  
Electric Effect ◽  
Electron Phonon Scattering

Makinson’s extension of Wilson’s treatment of the second-order effects in metals is used to derive an expression for the contribution of the lattice current to the thermo-electric power of metals at those temperatures where electron-phonon scattering predominates. It is found that in this temperature region one may expect the thermo-electric effect to show a sign opposite to the one which follows from the simple electron theory of metals. This is because the term due to the departure from equilibrium of the lattice distribution is larger than the usual term and is of opposite sign. If the temperature is greatly decreased or increased, the usual term predominates. The effect discussed may have a bearing on the behaviour of the thermo-electric power of the alkali metals, although it cannot explain this behaviour completely.

Electron diffraction from crystal defects: Fraunhofer effects from plane faults

1966 ◽  
Vol 293 (1433) ◽  
pp. 169-180 ◽  
Keyword(s):  
Electron Diffraction ◽  
Intensity Distribution ◽  
Stacking Faults ◽  
Dynamical Theory ◽  
Crystal Defects ◽  
Similar Calculation ◽  
Selected Area Electron Diffraction ◽  
Periodic Intensity ◽  
Diffraction Patterns ◽  
Calculated Intensity

The selected area electron diffraction patterns from a crystal containing a stacking fault have been observed to exhibit a number of unusual features. In some cases a periodic intensity distribution about the Bragg spot, in other cases streaking. By applying Kirchhoff’s theory of diffraction and using the dynamical theory of electron diffraction this intensity distribution around the Bragg spots in the electron diffraction patterns from stacking faults has been calculated. The calculated intensity distributions compare favourably with experiment. A similar calculation has also been carried out to predict the intensity distribution around Bragg spots in the selected area electron diffraction patterns from a crystal containing a grain boundary.

DIFFRACTION OF 3.2 CM. ELECTROMAGNETIC WAVES BY CYLINDRICAL OBJECTS

1954 ◽  
Vol 32 (6) ◽  
pp. 372-380 ◽  
Author(s):  
A. B. McLay ◽  
S. T. Wiles
Keyword(s):  
Electromagnetic Waves ◽  
Incident Beam ◽  
Diffraction Theory ◽  
Central Peak ◽  
Beam Direction ◽  
Cylinder Axis ◽  
Scalar Diffraction ◽  
Conducting Cylinder ◽  
Scalar Diffraction Theory ◽  
Diffraction Patterns

Diffraction patterns of a brass tube and a hard rubber rod, each a cylinder of 1 in. diameter, in a nearly plane beam of square-wave modulated 3 cm. waves with electric vector parallel to the cylinder axis, have been measured in several planes transverse to the incident beam direction. Experimental results for the conducting cylinder agree closely with calculations based on scalar diffraction theory. Patterns of the dielectric rod show a pronounced central peak immediately behind the rod and other intensity effects differing from the conducting cylinder patterns, particularly in the vicinity of the shadow.

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