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

An algebraic method for the determination of one-dimensional centrosymmetri c structures (or projections) of equal atoms has been extended to crystals without a centre of symmetry. The technique is an (almost) ab initio one, p rovides higher resolution than a Fourier map using the same number of struc ture factors, and permits either a unique solution compatible with the data employed or provides all possible solutions. It appears suitable in partic ular 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-dimensi onal projections plus from (at least) two rows parallel to the first ones f or three-dimensional structures.