4. Structure factor of diamond. The crystal structure of diamond is described in previous discussion. The basis consists of eight atoms if the cell is taken as the conventional cube. (a) Find the structure factor S of this basis. (b) Find the zeros of S and show that the allowed reflections of the diamond structure satisfy V₁ + V₂ + V3 = 4n, where all indices are even and n is any integer, or else all indices are odd (see figure below). Notice that h, k, I may be written for V₁, V₂, V3 and this is often done.

4. Structure factor of diamond. The crystal structure of diamond is described in previous discussion. The basis consists of eight atoms if the cell is taken as the conventional cube. (a) Find the structure factor S of this basis. (b) Find the zeros of S and show that the allowed reflections of the diamond structure satisfy V₁ + V₂ + V3 = 4n, where all indices are even and n is any integer, or else all indices are odd (see figure below). Notice that h, k, I may be written for V₁, V₂, V3 and this is often done.