Anomalous small-angle X-ray scattering of nanoporous two-phase atomistic models for amorphous silicon-germanium alloys

The present work deals with a detailed analysis of the anomalous small-angle X-ray scattering in amorphous silicon-germanium alloy using the simulation technique. We envisage the nanoporous two-phase alloy model consisting in a mixture of Ge-rich and Ge-poor domains and voids at the nanoscale. By substituting Ge atoms for Si atoms in nanoporous amorphous silicon network, compositionally heterogeneous alloys are generated with various composition-contrasts between the two phases. After relaxing the as-generated structure, we compute its radial distribution function, and then we deduce by the Fourier transform technique its anomalous X-ray scattering pattern. Using a smoothing procedure, the computed X-ray scattering patterns are corrected for the termination errors due to the finite size of the model, allowing so a rigorous quantitative analysis of the anomalous small-angle scattering. Our simulation shows that, as expected, the anomalous small-angle X-ray scattering technique is a tool of choice for characterizing compositional heterogeneities coexisting with structural inhomogeneities in an amorphous alloy. Furthermore, the sizes of the compositional nanoheterogeneities, as measured by anomalous small-angle X-ray scattering technique, are X-ray energy independent. A quantitative analysis of the separated reduced anomalous small-angle X-ray scattering, as defined in this work, provided a good estimate of their size.