513.001 Molecular and Solid State Physics

A two-dimensional crystal

A two dimensional crystal has a rectangular Bravais lattice (b = √2a) and a basis of two atoms which are located at 0 0 and 0.25 0.5. The electron densities of both atoms can be approximated by a gaussian function n(r) = 0.2 exp(-20(r/a)²). Calculate the structure factors of S(1 0), S(0 1), S(1 1), and S(1 2).