Question

4. Explain the relationship between the reciprocal and real lattices.

Answer 1

As we know that;

The reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice).

So,

Any repetitive and periodic distribution of a set of objects (or motifs) can be characterized, or described, by the translations that repeat the set of objects periodically. The implied translations generate what we call a direct lattice (or real lattice).

Then,

The relationship between the period and frequency is similar to that of the reciprocal and the direct lattice.

So,

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.