Lecture

Inside the powder diffraction pattern: XRD1

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Description

This lecture delves into the analysis of powder diffraction patterns, covering topics such as peak positions determined by the unit cell lattice, peak intensities influenced by atomic positions, and peak widths related to crystallite size and strain. It explains Bragg's law, structure factors, X-ray form factors, and Debye-Waller factors affecting peak intensities. The lecture also discusses peak shapes described by analytical functions and the fundamental parameters approach for separating contributions from source, instrument, and sample. It concludes with the analysis of sample texture in terms of crystallite size and strain.

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Related concepts (32)

Powder diffraction

Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials. An instrument dedicated to performing such powder measurements is called a powder diffractometer. Powder diffraction stands in contrast to single crystal diffraction techniques, which work best with a single, well-ordered crystal. Diffraction grating The most common type of powder diffraction is with x-rays, the focus of this article although some aspects of neutron powder diffraction are mentioned.

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.

Precession electron diffraction

Precession electron diffraction (PED) is a specialized method to collect electron diffraction patterns in a transmission electron microscope (TEM). By rotating (precessing) a tilted incident electron beam around the central axis of the microscope, a PED pattern is formed by integration over a collection of diffraction conditions. This produces a quasi-kinematical diffraction pattern that is more suitable as input into direct methods algorithms to determine the crystal structure of the sample.

Structure factor

In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns (interference patterns) obtained in X-ray, electron and neutron diffraction experiments. Confusingly, there are two different mathematical expressions in use, both called 'structure factor'.

Bragg's law

In physics and chemistry, Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a large crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals.

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