Wavelet analysis of x-ray diffraction pattern for glass structures

A wavelet analysis of x-ray diffraction patterns is introduced for analyzing glass structures. The analysis indicates that within a short distance (∼0.8 nm for silica glass) atoms in the glass are arranged around the most probable positions which are almost as regular as the equilibrium positions in crystal. However, in glass the atomic distribution around the most probable position increases exponentially with increasing interatomic distance (exponentially damped regularity), whereas the crystal does not have this kind of damping. Beyond this distance, it is difficult to determine the structure in atomic scale due to the large atomic distribution. But, the analysis shows that the arrangement of quasiatomic planes in glass is still statistically regular (with damped regularity) up to an intermediate distance, e.g., 2.5-3.0 nm for silica glass. Then glass structure might be quantitatively determined by means of the structure of corresponding crystals and of the extent of the distributions around the most probable positions for atoms, as well as of the sizes of the structurally correlated group.