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Reciprocal space (also called k-space) provides a way to visualize the results of the Fourier transform of a spatial function. It is similar in role to the frequency domain arising from the Fourier transform of a time dependent function; reciprocal space is a space over which the Fourier transform of a spatial function is represented at spatial frequencies or wavevectors of plane waves of the ...
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.
The translation vectors define the nodes of Bravais lattice. The lengths of principal axes/edges, of unit cell and angles between them are lattice constants, also called lattice parameters or cell parameters. The symmetry properties of crystal are described by the concept of space groups. [1]
Since Steno's Law can be further generalized for a single crystal of any material to include the angles between either all identically indexed net planes (i.e. vectors of the reciprocal lattice, also known as 'potential reflections in diffraction experiments') or all identically indexed lattice directions (i.e. vectors of the direct lattice ...
The X-ray diffraction patterns of aperiodic crystals contain two sets of peaks, which include "main reflections" and "satellite reflections". [1] Main reflections are usually stronger in intensity and span a lattice defined by three-dimensional reciprocal lattice vectors (,,).
In the Figure the red dot is the origin for the wavevectors, the black spots are reciprocal lattice points (vectors) and shown in blue are three wavevectors. For the wavevector k 1 {\displaystyle \mathbf {k_{1}} } the corresponding reciprocal lattice point g 1 {\displaystyle \mathbf {g_{1}} } lies on the Ewald sphere, which is the condition for ...
Ray diagram of Von Laue formulation. In physics, a Bragg plane is a plane in reciprocal space which bisects a reciprocal lattice vector, , at right angles. [1] The Bragg plane is defined as part of the Von Laue condition for diffraction peaks in x-ray diffraction crystallography.
An example of the tetragonal crystals, wulfenite Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system. In crystallography, the tetragonal crystal system is one of the 7 crystal systems.