fcc and bcc 1st Brillouin Zones

exercise 3_4950

(a) Find the ratio of the lengths of the diagonals of each parallelogram face of the first Brillouin zone (BZ) for the bcc lattice.

(b) Find the ratio of the length of an edge of the polyhedron bounding the first Brillouin zone (BZ) of the fcc lattice to the length of the conventional unit cell of the reciprocal lattice.

(c) Find the ratio of the volume of the 1 st BZ to the volume of the conventional unit cell of the reciprocal lattice for both the fcc and bcc lattices.