Reciprocal lattice

A lattice in reciprocal space whose vectors encode the periodicity of a crystal’s direct lattice and locate its diffraction peaks.

Diffraction condition: A constraint on scattered waves that determines when constructive interference produces a diffraction peak. Reciprocal-lattice points satisfy the scattering condition for peaks from a periodic crystal.
Crystal lattice: A periodic arrangement of points that represents the translational symmetry of a crystal. The reciprocal lattice is defined from this underlying periodic arrangement.
X-ray crystallography: A method for determining atomic structures by measuring X-ray diffraction from crystals. Measured diffraction spots map reciprocal-lattice points and their intensities.
Direct lattice: The real-space lattice of translations that describes a crystal's periodic structure. It describes positions in space, whereas the reciprocal lattice describes spatial periodicities.
Ewald sphere: A geometric construction in reciprocal space used to identify which reciprocal-lattice points satisfy elastic diffraction conditions. Its intersections with reciprocal-lattice points determine accessible diffraction peaks.
Primitive cell: The smallest-volume cell whose translations reproduce every point of a lattice. Its edge vectors generate a reciprocal primitive cell through cross products.
Neutron diffraction: A technique that probes material structures by scattering neutrons from atomic nuclei and magnetic moments. Neutron scattering peaks are indexed by reciprocal-lattice vectors.
Reciprocal space: A space whose coordinates represent spatial frequencies or wave vectors rather than physical positions. The reciprocal lattice is a discrete periodic structure embedded in this broader space.
Laue equations: Equations requiring scattered waves from a periodic crystal to interfere constructively along its lattice translations. They express the same diffraction constraints that reciprocal-lattice vectors encode geometrically.
Lattice plane: A family of parallel planes passing through lattice points in a crystal. Reciprocal vectors are perpendicular to lattice planes and encode their spacing.

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