AbstractAtomic pair-density function (PDF) analysis is an ideal 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 the local and complex structures of crystalline solids. Using PDF analysis, we demonstrate that important conclusions can be drawn about how the short-and long-range atomic structure of several oxide and hydrous oxide materials relates to their physical and electrochemical properties. For example, in Pb based ferroelectric relaxors, the diffraction pattern suggests a simple perovskite structure, while the PDF analysis shows that, in reality, the Pb atoms are strongly displaced from the high symmetry positions, so they can contribute to the electrical polarization. In hydrous ruthenium dioxide, RuO