Theoretical formulation of amorphous radial distribution function based on wavelet transformation

Atomic structure is an important parameter to analyze material physical properties, but investigating the atomic structure is not simple task, especially for disordered structure like amorphous material. Radial Distribution Function (RDF) calculation from experimental X-Ray Diffraction (XRD) data is generally chosen to investigate the disordered structure since RDF can count the number of atoms on each radial distance from arbitrary reference atom. However, when the X-Ray source is below 8 keV (short maximum wave vector q 8 Å-1), XRD data which uses Fourier Transformation (FT) will have low resolution. Therefore, we propose RDF calculation with Wavelet Transformation (WT) from our original wavelet function that was theoretically constructed using simple quantum model of interatomic bonding and semi-empirical method. Amorphous (Ge0.25Se0.75) and Agx(Ge0.25Se0.75)100-x with x = {5, 10, 15, 20, 25} were used as the validity check to compare the two RDF results from our model and the experimental XRD data. The comparison of the first and second peaks in our model and the experimental data indicates the minor error of our model approximately on 2.44% to 10.16%. This error range confirms the promising capability of our model to predict the atomic structure of disordered material like amorphous.