W0331

Determination of atomic structure is one of the first steps in materials research and characterization. If atoms are arranged periodically, as in most crystalline solids, its stucture can usually be determine by collecting X-ray or neutron diffraction pattern, and then indexing and comparing the result to the known database. If the structure is not known, a standard crystallographic method of structural refinement, like the Rietveld procedure, can be used for its determination.

Many materials of technical or scientific interest are strongly disordered or inhomogenous, yet these inhomogeneities or atomic disorder may be crucial for the material properties, making rigorous strutural charaterization critical. For disordered materials, diffraction patterns appear “amorphous” and distinction between crystalline and glassy structure can be difficult, so, it is impossible to pinpoint important structural features. While the X-ray absorption fine structure (EXAFS or XAFS) method can be used as a local structural probe and provide information about the immediate local environment (provided there is a suitable absorption edge), EXAFS has difficulties beyond first coordination shell.

Atomic pair-density function (PDF) analysis is an alternative approach for examining the local- and medium-range atomic structures of materials. PDF has been widely used in the studies of glasses and liquids and has also been applied successfully to characterize local and complex structures of crystalline solids. Using PDF analysis, we demonstrate that important conclusions can be drawn about short and long-range atomic structure and related to the physical and electrochemical properties of several oxide and hydroxide materials. For example in Pb based ferroelectric relaxors, the diffraction pattern suggests simple perovskites structure¹, while in reality Pb atoms are strongly displaced from high symmetry positions contributing to the electrical polarization. In hydrous ruthenium dioxide, RuO₂·xH₂O², standard X-ray diffraction pattern suggests apparent “amorphous” structure. However using PDF method, we demonstrate that the medium range structure of RuO₂·xH₂O is highly inhomogeneous, and it is best described as a network of ruthenium oxide nanocrystals dispersed by boundaries of structural water associated with Ru-O. We will provide several other examples of simple and effective use of PDF as well as discuss some technical issues related to data reduction.