Extending the power of powder diffraction for structure determination

Abstract

IN the modern techniques of high-resolution neutron and X-ray powder diffraction, an impressive amount of structural information may be obtained, allowing the refinement, using the Rietveld technique¹, of structures containing more than 100 positional parameters. Despite these technical advances and the renewed popularity of the technique, powder diffraction suffers from the inevitable loss of information imposed by the collapse of three dimensions of diffraction data onto the one dimension of a powder pattern. This can seriously frustrate the determination of unknown crystal structures. As a consequence of accidental or exact reflection overlap, only relatively few reflections may have uniquely determined intensities. (For example, the cubic reflections 550, 710 and 543 exactly overlap.) Here I present a maximum-entropy algorithm (previously discussed theoretically²) that evaluates, from first principles, the intensities of overlapping reflections in powder diffraction profiles. Indeed, a full three-dimensional reconstruction of the image may be retrieved when only ∼20% of the reflections are uniquely determined. This precludes systems where the Patter-son group is not the holosymmetric group (for example, the 4/m symmetry where hkl and khl reflections are overlapping but not equivalent.) Nevertheless, for most crystal structures with unit cell volumes of less than 1,000 ų, this method should be useful.