1.90: Reciprocal lattice
The reciprocal lattice is constituted by the set of all possible linear combinations of the basis vectors a* , b* , c* of the reciprocal space. A point ( node ), H , of the reciprocal lattice is defined by its position vector:
OH = r hkl * = h a* + k b* + l c* .
If H is the n th node on the row OH , one has:
OH = n OH 1 = n ( h 1 a* + k 1 b* + l 1 c* ),
where H 1 is the first node on the row OH and h 1 , k 1 , l 1 are relatively prime.
The generalization of the reciprocal lattice in a four-dimensional space for incommensurate structures is described in Section 9.8 of International Tables of Crystallography, Volume C .