Heavy atoms dominate the X-ray scattering from many inorganic compounds like oxides and oxalates, and often only partial structures of these compounds can be obtained by X-ray powder diffraction data. Combining information from X-ray and neutron diffraction data is an advantage. Scattering contributions from the atoms are more evenly distributed in neutron diffraction data than in X-ray diffraction data. Neutron diffraction data can then be used to complete a structure partially solved with data from an X-ray diffraction pattern. Examples of heavy atom structures solved in the time period 1983–2004 using direct methods outlined above are presented.

Crystal structure of Ca1.1Co1.9(PO4)2 was successfully determined from laboratory X-ray powder diffraction data (Co Kα) using direct methods and the Rietveld refinement. The crystal structure was found to be monoclinic (space group P21∕n, Z=4) with lattice dimensions of a=1.452 67(5) nm, b=0.494 34(1) nm, c=0.867 50(3) nm, β=92.316(1)°, and V=0.622 45(3) nm3. The final reliability indices calculated from the Rietveld refinement were Rwp=3.93%, Rp=3.02%, RB=4.10%, and S=1.48. Both Co and Ca atoms were distributed over the 2a and 2d sites with a preference of Ca at the 2d site. The coexistence of Co and Ca on the 2a and 2d sites is indispensable for stabilizing Ca1.1Co1.9(PO4)2 in the Ca3(PO4)2-Co3(PO4)2 system.

Ab initio crystal structure solution by powder diffraction data is based on the experimental full pattern decomposition process: the resulting structure factor moduli are used for direct phasing. The extracted intensity estimates are scarcely accurate (overlapping, background, and preferred orientation are the main causes of the lack of accuracy), no matter if Le Bail or Pawley method is adopted: consequently the structure solution process is not straightforward. We have focused our attention on the relation between the efficiency of the EXPO2004 phasing process and the various parameters which are normally used in the full pattern decomposition process, e.g., the peak shape function, the number of refinement cycles, the degree of overlapping. Different steps of the phasing process are considered: the definition of the unit cell, the determination of the space group, and the application of direct methods.

Kinematical and two-beam calculations have been conducted and are compared to experimental precession data for the large unit cell crystal La4Cu3MoO12. Precession electron diffraction intensities are found to exhibit approximate two-beam behavior and demonstrate clear advantages over conventional SADP intensities for use in structure solution.

We investigate cases where one can argue that sufficient conditions exist for Direct Methods to work with swift electrons. In addition to simple cases where kinematical scattering holds (e.g., surfaces in plan view), we identify three other configurations: (a) when 1s channeling holds and kinematical scattering is statistically correct; (b) when there is a mapping from kinematical to dynamical intensities that preserves the order of the intensities, for instance with powder or precession data, and (c) when the scattering is dominated by one type of atom. We also briefly discuss the possibility of using Direct Methods to restore the complex exit wave leaving a sample in the most general case.