Solving crystal structures without Fourier mapping. II. Non-centrosymmetric case

Abstract

An algebraic method for the determination of one-dimensional centrosymmetric structures (or projections) of equal atoms has been extended to crystals without a centre of symmetry. The technique is an (almost) ab initio one, provides higher resolution than a Fourier map using the same number of structure factors, and permits either a unique solution compatible with the data employed or provides all possible solutions. It appears suitable in particular for partial structures with not too many atoms per asymmetric unit (e.g. anomalous scatterers in a “biological“ crystal structure). It only needs rather selected data: from central reciprocal lattice rows for one-dimensional projections plus from (at least) two rows parallel to the first ones for three-dimensional structures.