Small-Angle X-Ray Scattering of Amorphous Germanium: Numerical Modeling

摘要

The present work deals with a detailed analysis of the small-angle X-ray scattering of nanoporous atomistic models for amorphous germanium. Structures with spherical nanovoids, others with arbitrarily oriented ellipsoidal ones, with monodisperse and polydisperse size distributions, were first generated. After relaxing the as-generated structure, we compute its radial distribution function, and then we deduce by the Fourier transform technique its X-ray scattering pattern. Using a smoothing procedure, the computed small-angle X-ray scattering patterns are corrected for the termination errors due to the finite size of the model, allowing so, for the first time at our best knowledge, a rigorous quantitative analysis of this scattering. The Guinier’s law is found to be valid irrespective of size and shape of the nanovoids over a scattering vector-range extending beyond the expected limit. A weighted combination of the Guinier’s forms accounts for well the nanovoid size distribution in the amorphous structure. The invariance of the Q-factor and its relationship to the void volume fraction are also confirmed. Our findings support then the quantitative analyses of available small-angle X-ray scattering data for amorphous germanium.