Atomic-Scale Structure of Glasses Using High-Energy X-Ray Diffraction

KNOWLEDGE of the atomic-scale structure is an important prerequisite to understand and control the properties of materials. In the case of crystals, it is obtained solely from the Bragg peaks in their diffraction pattern and is given in terms of a small number of atoms placed in a unit cell subjected to symmetry constraints. However, many materials of technological importance, such as glasses, do not possess the long-range order of conventional crystals and often it is this deviation from perfect order that makes them technologically and/or scientifically important. The diffraction patterns of such non-crystalline materials show only a few sharp, Bragg-like peaks, if any, and a pronounced diffuse component. This renders the standard crystallography and techniques for structure determination inapplicable. The challenge can be met by using the so-called atomic pair distribution function (PDF) technique. The widely used atomic PDF, G(r), is defined as G(r) 5 4pr[r(r) r0], where r(r) and r0 are the local and average atomic number densities, respectively. It peaks at real space distances where the local atomic density deviates from the average one, i.e., where most frequent interatomic distances occur, and thus reflects the structure of materials. Atomic PDFs are obtained by neutron or X-ray diffraction experiments. A PDF is computed from the diffraction data via a Fourier transformation as follows: