A method for obtaining a possibly unique (unambiguous) crystal structure solution using multiple resonant scattering data

A sequence of steps for determining a crystal structure, possibly without ambiguities, is presented. The prerequisites are: centrosymmetry (at present) and two different anomalous scatterers, a(1), a(2). Their partial structure amplitudes \F-a1(hkl)\ and \F-a2(hkl)\ are separated by multiple-wavelength measurements (MAD). The core part of the method is a recursive algebraic technique applied to the geometrical part of these structure amplitudes from central reciprocal-lattice rows. At least m + 1 reflections are necessary at each row if 2m atoms of e.g. a(1) are in a unit cell with space group P (1) over bar. For each partial structure of a(1) and a(2) atoms, respectively, the algebra finds all homometric and pseudohomometric solutions and presents the corresponding signs for each F-a(hkl) used. Regions of confidence for atomic coordinates are given. Five reciprocal-lattice rows (or more) suffice for a 'tomographic' location of all atoms a(1) and a(2) in three dimensions. The two independently determined partial structures for a(1) and a(2) are then aligned to the same origin and moduli plus signs of the remaining partial structure factors of the non-resonant atoms are determined. Various aspects of the method are discussed by application to the Cu3SbSe3 structure, an example exhibiting partial pseudosymmetry.