Reciprocal Lattice

The reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice). In normal usage, this first lattice (whose transform is represented by the reciprocal lattice) is usually a periodic spatial function in real-space and is also known as the direct lattice.Reciprocal space is also called Fourier space, k- space, or momentum space in contrast to real space or direct space. 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 = rhkl* = h a* + k b* + l c*.

If H is the nth node on the row OH, one has:

OH = n OH1 = n (h1 a* + k1 b* + l1 c*),

where H1 is the first node on the row OH and h1 , k1 , l1 are relatively prime.

The reciprocal space lattice is a set of imaginary points constructed in such a way that the direction of a vector from one point to another coincides with the direction of a normal to the real space planes and the separation of those points (absolute value of the vector) is equal to the reciprocal of the real interplanar distance.