513.001 Molecular and Solid State Physics

Structure factors of a two-dimensional function

Circles of radius R are placed at every point of a two dimensional hexagonal Bravais lattice. The radii of the circles is small enough that the circles do not overlap. A two-dimensional periodic function is defined such that it is a constant C inside the circles and zero outside the circles. This periodic function can be written in the form,

where the G's are the reciprocal lattice vectors and f_G's are the structure factors. Determine the structure factors for this periodic function.

See Fourier series in 2-D and 3-D for a discussion of Fourier series.