Combined effects of homogenization and singular perturbations: A bloch wave approach

AbstractIt is shown how the use of a high angle annular detector in a STEM provides images which show strong compositional sensitivity and almost perfect incoherent characteristics. No contrast reversals occur with defocus or sample thickness and the contribution of an atomic string is insensitive to the distribution and strength of neighboring strings. The image is best described in real space as a simple convolution of the incident probe intensity profile with an object function sharply peaked at the atomic strings having a strength dependent on composition. How the incoherent characteristics arise is described using a Bloch wave approach and examples are shown of interfaces in semiconductor and superconductor materials.

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Combined effects of homogenization and singular perturbations in elasticity.

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.1994.454.1 ◽

1994 ◽

Vol 1994 (454) ◽

pp. 1-36 ◽

Cited By ~ 1

Keyword(s):

Singular Perturbations ◽

Combined Effects

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Electron-Channelling Patterns: Principles and Techniques

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100091986 ◽

1976 ◽

Vol 34 ◽

pp. 400-401

Author(s):

David C. Joy

Keyword(s):

Crystal Structure ◽

Electron Flux ◽

Lattice Structure ◽

Incident Beam ◽

Bloch Wave ◽

Crystalline Solid ◽

Angle Of Incidence ◽

Electron Channelling ◽

Regular Arrangement ◽

Backscattered Signals

In a crystalline solid the regular arrangement of the lattice structure influences the interaction of the incident beam with the specimen, leading to changes in both the transmitted and backscattered signals when the angle of incidence of the beam to the specimen is changed. For the simplest case the electron flux inside the specimen can be visualized as the sum of two, standing wave distributions of electrons (Fig. 1). Bloch wave 1 is concentrated mainly between the atom rows and so only interacts weakly with them. It is therefore transmitted well and backscattered weakly. Bloch wave 2 is concentrated on the line of atom centers and is therefore transmitted poorly and backscattered strongly. The ratio of the excitation of wave 1 to wave 2 varies with the angle between the incident beam and the crystal structure.

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Convergent-beam electron diffraction at high spatial resolution

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100130390 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1152-1153 ◽

Cited By ~ 1

Author(s):

J W Steeds

Keyword(s):

Electron Diffraction ◽

High Temperature Superconductors ◽

Bloch Wave ◽

Convergent Beam Electron Diffraction ◽

Beam Electron ◽

Energy Filtering ◽

Small Probe ◽

Transmission Electron ◽

Electron Microscopes ◽

Convergent Beam

That the techniques of convergent beam electron diffraction (CBED) are now widely practised is evident, both from the way in which they feature in the sale of new transmission electron microscopes (TEMs) and from the frequency with which the results appear in the literature: new phases of high temperature superconductors is a case in point. The arrival of a new generation of TEMs operating with coherent sources at 200-300kV opens up a number of new possibilities.First, there is the possibility of quantitative work of very high accuracy. The small probe will essentially eliminate thickness or orientation averaging and this, together with efficient energy filtering by a doubly-dispersive electron energy loss spectrometer, will yield results of unsurpassed quality. The Bloch wave formulation of electron diffraction has proved itself an effective and efficient method of interpreting the data. The treatment of absorption in these calculations has recently been improved with the result that <100> HOLZ polarity determinations can now be performed on III-V and II-VI semiconductors.

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A Stationary Solution of High-Energy Electron Reflection (HEER) for An Arbitrary Surface

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100135472 ◽

1990 ◽

Vol 48 (2) ◽

pp. 374-375

Author(s):

YIQUN MA

Keyword(s):

Stationary Solution ◽

High Energy ◽

Bloch Wave ◽

Dynamical Theory ◽

High Energy Electron ◽

Bulk Materials ◽

Periodic Surface ◽

Electron Transmission ◽

Electron Reflection ◽

Long Time

For a long time, the development of dynamical theory for HEER has been stagnated for several reasons. Although the Bloch wave method is powerful for the understanding of physical insights of electron diffraction, particularly electron transmission diffraction, it is not readily available for the simulation of various surface imperfection in electron reflection diffraction since it is basically a method for bulk materials and perfect surface. When the multislice method due to Cowley & Moodie is used for electron reflection, the “edge effects” stand firmly in the way of reaching a stationary solution for HEER. The multislice method due to Maksym & Beeby is valid only for an 2-D periodic surface.Now, a method for solving stationary solution of HEER for an arbitrary surface is available, which is called the Edge Patching method in Multislice-Only mode (the EPMO method). The analytical basis for this method can be attributed to two important characters of HEER: 1) 2-D dependence of the wave fields and 2) the Picard iteractionlike character of multislice calculation due to Cowley and Moodie in the Bragg case.

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Effects of Higher-Order Laue Zone reflections on structure images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148083 ◽

1993 ◽

Vol 51 ◽

pp. 450-451

Author(s):

H. S. Kim ◽

S. S. Sheinin

Keyword(s):

Wave Vector ◽

Theoretical Calculations ◽

Reciprocal Lattice ◽

Image Plane ◽

Bloch Wave ◽

Dynamical Theory ◽

Higher Order ◽

Lattice Image ◽

Lattice Vector ◽

Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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