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A powder X-ray diffractometer in motion. X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract in specific directions.
Typically, powder X-ray diffraction (XRD) is an average of randomly oriented microcrystals that should equally represent all crystal orientation if a large enough sample is present. X-rays are directed at the sample while slowly rotated that produce a diffraction pattern that shows intensity of x-rays collected at different angles.
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern.
The incoming beam (coming from upper left) causes each scatterer to re-radiate a small portion of its intensity as a spherical wave. If scatterers are arranged symmetrically with a separation d, these spherical waves will be in sync (add constructively) only in directions where their path-length difference 2d sin θ equals an integer multiple of the wavelength λ.
Consider the scattering of a beam of wavelength by an assembly of particles or atoms stationary at positions , =, …,.Assume that the scattering is weak, so that the amplitude of the incident beam is constant throughout the sample volume (Born approximation), and absorption, refraction and multiple scattering can be neglected (kinematic diffraction).
100: 1,000: Fermi Surface Shape Resonant IXS (RIXS) 4-20: 0.1 - 50: Electronic Structure & Excitations Non-Resonant IXS (NRIXS) 10: 0.1 - 10: Electronic Structure & Excitations X-ray Raman scattering: 10: 50 - 1000: Absorption Edge Structure, Bonding, Valence High resolution IXS: 10: 0.001 - 0.1: Atomic Dynamics, Phonon Dispersion
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