Structure-refinement program for disordered carbons

An automated structure-refinement program has been developed for X-ray powder diffraction data collected on disordered carbons. The program minimizes the difference between the observed and calculated diffraction profiles in a least-squares sense by optimizing model parameters analogously to the popular Rietveld refinement method. Unlike the Rietveld method, which is designed for crystalline materials, this program allows the quantification of the finite size, strain and disorder present in disordered carbon fibers and cokes. For example, the structural model used includes the probability of a random translation parallel to adjacent carbon layers as a refinable parameter describing turbostratic disorder. Other parameters are used to describe finite size, fluctuations in the spacing between adjacent layers, average lattice constants, background and other important quantities. The structural model, combined with the refinement program, acceptably describes the diffraction patterns from disordered carbons such as pitch heated near 823 K, cokes, fibers, heat-treated cokes and synthetic graphite.