A quasi-crystalline model for interpretation of radial distribution functions: theory and experimental confirmation

A quasi-crystalline model has been developed which facilitates calculation of the intensity and radial distribution functions (RDF) for hypothetical molecular arrangements in glasses. Interatomic distances are counted so that each atom in the asymmetric unit `sees' all the other atoms within a given radius of that atom, thus eliminating the edge effects inherent in simply counting all possible interatomic distances between atoms in a finite block of crystal. A disorder parameter is associated with each interatomic distance and incorporates thermal motion and the loss of correlation between atoms with increasing distance due to the non-periodic nature of amorphous substances. The RDF calculated for the high albite (NaAlSi₃O₈) structure is in good agreement with the RDF determined experimentally on a polycrystalline sample. Spurious ripples, which are larger than can be explained by termination of the Fourier integral, are observed in the experimental RDF's and suggest a systematic error of 3-5% in the corrected diffraction profile. No single source of error (e.g. scaling, absorption, polarization, background estimation) can account for the observed ripples, but a combination of these sources might result in an error of the magnitude suggested.