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Lecture# Dynamical Scattering

Description

This lecture covers the concept of dynamical scattering in electron diffraction, where electrons interact strongly with matter, leading to multiple scattering events. The lecture explains how scattering and intensities in different diffracted beams are interdependent, making interpretation challenging. Topics include thickness fringes, bend contours, double diffraction, and crystal phase discrimination. Examples are provided to illustrate these phenomena, such as the formation of satellite spots and bend contours in dark-field images. The lecture also discusses the applications of electron diffraction in studying crystal defects, crystal phases, and epitaxial relationships.

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Related concepts (54)

Related lectures (17)

Diffraction

Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

Electron diffraction

Electron diffraction refers to changes in the direction of electron beams due to interactions with atoms. Close to the atoms the changes are described as Fresnel diffraction; far away they are called Fraunhofer diffraction. The resulting map of the directions of the electrons far from the sample (Fraunhofer diffraction) is called a diffraction pattern, see for instance Figure 1. These patterns are similar to x-ray and neutron diffraction patterns, and are used to study the atomic structure of gases, liquids, surfaces and bulk solids.

Fraunhofer diffraction

In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer condition) from the object (in the far-field region), and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object and (in the near field region) is given by the Fresnel diffraction equation.

Fresnel diffraction

In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, F, of the optical arrangement.

Crystallographic defect

A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect. Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization.

Electron Diffraction: Basics & Applications

Explores electron diffraction basics, including Bragg's law, reciprocal lattice, and applications like crystal phase discrimination.

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Covers electron diffraction theory, Bragg's law, reciprocal lattice, Ewald sphere, and weak-beam dark-field imaging.

Electron Diffraction: Basics & Applications

Covers the basics of electron diffraction, explaining contrast in TEM images and its applications in material analysis.

Electron Diffraction: Basics & Applications

Explores electron diffraction fundamentals, crystal symmetry, and advanced techniques for materials analysis.

Dynamical Scattering: Electron Diffraction

Explores dynamical scattering in electron diffraction, discussing challenges in interpreting diffraction patterns and applications in crystal defect imaging and phase discrimination.