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In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength ...
In X-ray crystallography, wide-angle X-ray scattering (WAXS) or wide-angle X-ray diffraction (WAXD) is the analysis of Bragg peaks scattered to wide angles, which (by Bragg's law) are caused by sub-nanometer-sized structures. [1] It is an X-ray-diffraction [2] method and commonly used to determine a range of information about crystalline materials.
The dynamical theory of diffraction considers the wave field in the periodic potential of the crystal and takes into account all multiple scattering effects. Unlike the kinematic theory of diffraction which describes the approximate position of Bragg or Laue diffraction peaks in reciprocal space , dynamical theory corrects for refraction, shape ...
The Laue equations can be written as = = as the condition of elastic wave scattering by a crystal lattice, where is the scattering vector, , are incoming and outgoing wave vectors (to the crystal and from the crystal, by scattering), and is a crystal reciprocal lattice vector.
When the incident light beam is at Bragg angle, a diffraction pattern emerges where an order of diffracted beam occurs at each angle θ that satisfies: [3] = Here, m = ..., −2, −1, 0, +1, +2, ... is the order of diffraction, λ is the wavelength of light in vacuum, and Λ is the wavelength of the sound. [4]
X-ray crystal truncation rod scattering is a powerful method in surface science, based on analysis of surface X-ray diffraction (SXRD) patterns from a crystalline surface. For an infinite crystal , the diffracted pattern is concentrated in Dirac delta function like Bragg peaks .
where the magnitude of the scattering vector q is in reciprocal lattice distance units, N is the number of atoms, f i (q) is the atomic scattering factor for atom i and scattering vector q, while r ij is the distance between atom i and atom j. One can also use this to predict the effect of nano-crystallite shape on detected diffraction peaks ...
where G, R g, and B are constants related to the scattering contrast, structural volume, surface area, and radius of gyration. q is the magnitude of the scattering vector which is related to the Bragg spacing, d, q = 2π/d = 4π/λ sin(θ/2). λ is the wavelength and θ is the scattering angle (2θ in diffraction).