A lattice for a crystal that can be defined from the lattice in real space. If the primitive translation vectors of the lattice in real space are denoted by a, b, c then the primitive translations a′, b′, c′ in the reciprocal lattice are defined by a′=b × c[abc], b′=c × a[abc], c′=a × b[abc], where [abc] denotes the scalar triple product a.(b × c).

The reciprocal lattice is a fundamental concept in the theory of X-ray diffraction and energy bands with a diffraction pattern being much more closely related to the reciprocal lattice than the real-space lattice. Thus, the concept of the reciprocal lattice clarifies and simplifies the theory of X-ray diffraction by crystals in three dimensions.