Medium range order and the radial distribution function

We have studied the subtle differences between the radial distribution functions g(r) of several models of disordered silicon, which contain differing amounts of paracrystalline medium range order. Due to the inherent averaging of diffraction data at medium range length scales r, the differences are indeed small. We find, however, that the residual function G(r) = r[g(r) - 1] exhibits an oscillatory decay, with discernibly different decay lengths. The decay lengths are found to be proportional to the radial extent of the medium range order in the model as determined by several other computational methods. Our results indicate that the extent of medium range order could be measured by diffraction experiments. However, to discern the nature of the ordering, fluctuation microscopy is needed, and for models, improved methods for modeling the oscillatory part of G(r) are essential.