An efficient ab initio calculation of powder diffraction intensity using Debye's equation

The Debye equation gives the spherically averaged diffracted intensity from a group of atoms and is exact under the first Born, or kinematic, approximation. Algebraic simplifications are developed for calculating multiplicities in the double summation and are used in a new algorithm for implementing this equation. The results for cubic, body-centred cubic and face-centred cubic systems agree exactly with previous methods while achieving substantial computational advantage.