(Solved): 2. Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may b ...

2. Hexagonal space lattice. The primitive translation vectors of the hexagonal space lattice may be taken as a3 = cz. a? = (3¹/2a/2) + (a/2)? ; a? = ?(3¹/2a/2) + (a/2)? ; (a) Show that the volume of the primitive cell is (3¹/2/2)a²c. (b) Show that the primitive translations of the reciprocal lattice are b? = (2?/3¹/2²a)x + (2?/a)? ; b? = ?(2?/3¹a) + (2?/a)? ; 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. b3 = (2?/c)2,