Q1: If the primitive translation vectors of the space lattice may be taken as a, = (31/29x + )y %3D az = - (3/2)x y az = cz Based on the reciprocal lattice principle, find: 1. The volume of the primitive cell? 2. The primitive translation s of the reciprocal lattice ?

Question 3 Consider the simple and close-packed hexagonal direct lattices. (a) Find out the general expression for the structure factor for each lattice type. In this context, what is the significance of a complex structure factor? (b) Without resorting to the structure factor, determine in which structure(s) X-ray Bragg reflections arise from the lattice planes (0001), (0002), and (1010). Justify your answer by the use of the above determined structure factor or otherwise and explain the meaning of the four indices describing the above cited lattice planes.

4. Consider a simple cubic system with lattice constant a = 5 Å. Determine the atom density (atoms/cm²) for the (100), (110), and (111) planes.

Q1. Find the divergence of D for the following D distributions. А. e* sin yx-е" cos y y+ 2-z 4xy, 2x2 2x'y В. x+- y-