Question

(b) A caesium-bromide crystal has a simple cubic lattice with lattice constant a= 4.30 A. The basis of the crystal contains one caesium atom at fi = (0,0,0) and one bromine atom at r2 = (a/2, 2/2,a/2), where the vectors and are expressed with respect to the Cartesian basis vectors i, j, k. (i) The relative atomic mass of Cs is 133 amu and the relative atomic mass of Br is 80.0 amu, where I amu = 1.66 x 10-2 kg. Calculate the density of the crystal, giving your answer in gem (ii) Sketch the reciprocal lattice of the crystal in the r-y plane. Indicate the dimensions of the reciprocal lattice in units of A- Determine the reciprocal lattice vectors a", b' and e'. Include these vec- tors in your sketch if they lie in the r-y plane. (iii) Describe the size and shape of the first Brillouin zone of the lattice.