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Lecture# Electron Diffraction: Basics and Applications

Description

This lecture covers the fundamentals of electron diffraction, including the importance of electron diffraction in TEM images, Bragg's law, reciprocal lattice, Ewald sphere, multiple beam scattering, and deviation from Bragg condition. It also explores the applications of electron diffraction in understanding crystal structures and symmetry. The instructor explains the concept of lattice points, unit cells, crystal systems, and centering types in crystallography. The lecture delves into lattice vectors, lattice planes, and interplanar spacings in cubic crystals. Additionally, it discusses the effect of sample shape on diffraction patterns and the techniques for setting dark-field imaging conditions.

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Related concepts (164)

Related lectures (69)

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Reciprocal lattice

In physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where refers to the wavevector. In quantum physics, reciprocal space is closely related to momentum space according to the proportionality , where is the momentum vector and is the reduced Planck constant.

Crystal structure

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter. The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure.

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.

Miller index

Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and l, the Miller indices. They are written (hkl), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to , where are the basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice.

X-ray crystallography

X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the mean positions of the atoms in the crystal can be determined, as well as their chemical bonds, their crystallographic disorder, and various other information.

Deviation from Bragg scattering

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

Electron Diffraction: Basics & Applications

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

Electron Diffraction: Basics & Applications

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

Reciprocal Lattice and Diffraction

Explores reciprocal lattice in 2D systems, diffraction from lattice and atomic structures, emphasizing scattering and constructive interference.

Electron Diffraction: Basics & Applications

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