Indexing 2D Powders and Lagrange-Gauss Reduction

2D powders constitute an important class of molecular thin films where a specific close-packed plane forms parallel to the substrate surface, while there is no preferred lateral ordering. Using results from classic lattice reduction theory, a systematic scheme is proposed, in order to determine the surface unit cell for 2D powders in reciprocal space. The approach is based on a sorted set of scattering vector lengths 𝑞1, 𝑞2, 𝑞3, … directly obtained from the scattering pattern. After a first match is established, a refinement procedure is presented that makes full use of the complete set of scattering vectors and as such corrects for small experimental errors and ensures a good overall match with the observed reflections.