The primitive translation vectors of the hexagonal space lattice may be taken as a = (3a/2) + (a/2) ; a = -(3a/2)& + (a/2) ; az = c . (a) Show that the volume of the primitive cell is (3/2)a*c. (b) Show that the primitive translations of the reciprocal lattice are b (2m/3a)& + (27la) ; b = -(2m/3a) + (2mla) ; b, = (2m/c) , %3D so that the lattice is its own reciprocal, but with a rotation of axes. (c) Describe and sketch the first Brillouin zone of the hexagonal space lattice.