TITLE:
Small-Angle X-Ray Scattering of Amorphous Germanium: Numerical Modeling
AUTHORS:
R. Ben Brahim, A. Chehaidar
KEYWORDS:
Amorphous Germanium; Structure; Small-Angle X-Ray Scattering; Modeling
JOURNAL NAME:
Advances in Materials Physics and Chemistry,
Vol.3 No.1A,
April
26,
2013
ABSTRACT: 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.