PH-409 (2015) Tutorial Sheet No. 2 * Problems shall be discussed in tutorial class 20*.A two dimensional lattice has basis vectors ˆˆˆ2 ; 2aibij. Find the basis vectors of the reciprocal lattice. 21.(a) Show that the reciprocal lattice of the reciprocal lattice is the original direct lattice. (b) Find the reciprocal lattice of a one dimensional lattice with spacing 'a'. Also find the first Brillouin Zone. 22. Show that the reciprocal lattice to orthorhombic; 90oabcac-face centered lattice, having the following primitive vectors, is another orthorhombic c-face centered lattice. ˆˆˆˆ; 22abaaibij cck23.Draw the first four Brillouin zones of a two dimensional square lattice and show that they are of equal area. 24*. Consider a plane hkin a crystal lattice. (a) Prove that the reciprocal lattice vector GhAkBCis normal to this plane. (b) Show that the distance between two adjacent (ℎ??)planes of the lattice is given by the following. ; 2 hk d G (c) Using (b) show for a simple cubic lattice the following relationship. 222adhk25.A simple orthorhombic lattice is characterized by following primitive vectors. ˆˆˆ; ; ; abcaaaibbj cckFind the angle between [ℎ??]direction and normal to the (ℎ??)planes.