Indexing 2D Powders and Lagrange–Gauss Reduction

Two-dimensional (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 3D surface unit cell for 2D powders in reciprocal space. The approach is based on a sorted set of lengths q1,q2,q3,… of the in-plane components of the scattering vector, which is 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. After identifying the in-plane components, the full 3D surface unit cell can be found in a straightforward way.