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 with out 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 metho d is a recursive algebraic technique applied to the geometrical part o f 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 part ial structure of a(1) and a(2) atoms, respectively, the algebra finds all homometric and pseudohomometric solutions and presents the corresp onding 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 dimen sions. The two independently determined partial structures for a(1) an d a(2) are then aligned to the same origin and moduli plus signs of th e remaining partial structure factors of the non-resonant atoms are de termined. Various aspects of the method are discussed by application t o the Cu3SbSe3 structure, an example exhibiting partial pseudosymmetry .