Uncovering the intrinsic geometry from the atomic pair distribution function of nanomaterials

Atomic pair distribution functions are useful because they have an easy intuitive interpretation and can be obtained both experimentally and from computer-generated structure models. For bulk materials, atomic pair distribution functions are solely determined by the intrinsic atomic geometry, i.e., how atoms are positioned with respect to one another. For a nanomaterial, however, the atomic pair distribution function also depends on the shape and size of the nanomaterial. A modified form of the radial distribution function is discussed that decouples shape and size effects from intrinsic effects so that nanomaterials of any shape and size, sharing a common atomic geometry, map onto a universal curve, by using a form factor. Mapping onto this universal curve allows differences in the intrinsic atomic geometry of nanomaterials of various shapes and sizes to be directly compared. This approach is demonstrated on nanoscale amorphous and crystalline silica models. It is shown how form factors can be computed for arbitrary shapes and this is illustrated for tetrahedral nanoparticles of vitreous silica.