  ## 4.5 Reciprocity of F and I lattices

Let us consider a face-centered lattice. It is well known that the basic vectors a , b , c , of the elementary cell are given in terms of the vectors a, b, c of the face centered cell by (Fig. 5): (4.4)

In a similar way, the basic vectors a ,b , c of the elementary cell of a body centered lattice are given in terms of the basic vectors of the multiple cell by (Fig. 6): (4.5)

Let us now look for the reciprocal lattice of the face-centered lattice. Its unit cell vectors are given by, using (2.1) and (4.4): (4.6)  Noting that the face-centered cell is of the fourth order, we find: We may thus express a * in terms of the basic vectors of the reciprocal lattice of the lattice of vectors a, b, c: This may also be written: This relation shows that the reciprocal lattice of a face-centered lattice is a body centered lattice whose multiple cell is defined by 2a*, 2b*, 2c*. If we index the reciprocal lattice defined by a*, b*, c*, that is the reciprocal lattice of the multiple lattice defined by a, b, c, we find that only the nodes such that belong to the reciprocal lattice of the face-centered lattice. This shows that the only Bragg reflexions on a face-centered lattice have indices which are all of the same parity.   Next: 5. Diffraction Condition in the Reciprocal Up: 4. Crystallographic Calculations Using the Reciprocal Previous: 4.4 Zone axis of two sets