Nanoscale structural order from the atomic pair distribution function (PDF): Thereʹs plenty of room in the middle

Emerging materials of scientific and technological interest are generally complex and often nanostructured: they have atomic orderings that extend on nanometer length-scales. These can be discrete nanoparticles; bulk crystals with nanoscale chemical or displacive order within them; mesoporous materials that are bulk materials containing nanoscale holes; and nanocomposites that are intimate heterogeneous mixtures of nano-sized constituents. As always, a quantitative knowledge of the atomic structure within these materials is a prerequisite to understanding and engineering their properties. Traditional crystallographic methods for obtaining this information break down at the nanoscale, sometimes referred to as “the nanostructure problem”. We describe here some emerging methods for studying nanoscale structure. We present some examples of recent successes. Finally, we discuss future directions and opportunities and draw attention to limitations and potential problems.