Orientational order in dense random sphere packings

One possible model for the structure of amorphous metals is a dense random packing of hard spheres. For equal spheres, this model yields a radial distribution function (RDF) that agrees well with the experimental RDF for amorphous ${\mathrm{Ni}}_{80}$ ${\mathrm{P}}_{20}$. However, since different models of the atomic structure of amorphous metals may produce different RDF’s, it is important to find a way to distinguish between these models. One possibility is orientational order. Eventually experiments will determine which model is correct, but the appropriate experiments have not yet been done. Therefore we have performed a series of ‘‘computer experiments’’ on the dense random packing of hard spheres to see if there is any icosahedral (or other) orientational order. These computer experiments were performed on computer generated dense random packings of binary mixtures of hard spheres, with from 1000 to 2000 spheres, size ratios from 1.0 to 2.0, and composition fractions from 20% to 80% small spheres. We measure orientational order using two different methods. One is graphical and uses a local coordinate system for each sphere; the other is quantitative and uses a fixed reference coordinate system. The second method is the orientational order parameter formalism as defined by Steinhardt, Nelson, and Ronchetti. The graphical and quantitative methods provide complementary measures of the orientational order present in our dense random sphere packings. Both methods indicate that there is negligible icosahedral order on any scale in any of the packings.