Structure of crystallographically challenged materials by profile analysis of atomic pair distribution functions: study
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Structure of crystallographically challenged materials by profile analysis of atomic pair distribution functions: study of LiMoS2 and mesostructured MnGe4S10. V.Petkov1,3, K. K. Rangan2,3, M. G. Kanatzidis2,3 and S.J.L. Billinge1,3 1
Department of Physics and Astronomy, 2Department of Chemistry and 3Center for Fundamental Materials Research, Michigan State University, East Lansing, MI-48824
Abstract The approach of the atomic pair distribution function (PDF) technique to study the structure of materials with significant disorder is considered and successfully applied to LiMoS2 and mesostructured MnGe4S10. We find that LiMoS2 is built of layers of distorted MoS6 octahedra stacked along the c axis of a triclinic unit cell with well-defined Mo-Mo bonding. Mesostructured MnGe4S10 is a three-dimensional framework of "adamantane-like" [Ge4S10] units bridged by Mn atoms. Introduction Many materials of technological importance are not perfectly crystalline but contain significant disorder at the atomic scale. The diffraction patterns of such materials show a pronounced diffuse component and only a few Bragg peaks. This poses a real challenge to the usual techniques for structure determination. The challenge can be met by employing the so-called atomic pair distribution function (PDF) technique. The atomic PDF gives the number of atoms in a spherical shell of unit thickness at a distance r from a reference atom. It peaks at characteristic distances separating pairs of atoms and thus describes the structure of materials. The PDF, G(r)=4πr[ρ(r)-ρo], is the sine Fourier transform of the so-called total scattering structure function, S(Q), G(r)=(2/π)
Qmax
∫ Q[ S (Q ) − 1] sin(Qr)dQ,
(1)
Q =o
where ρ(r) and ρo are the local and average atomic number densities, respectively, Q is the magnitude of the wave vector and S(Q) is the corrected and properly normalized total powder diffraction pattern of the material [1]. As can be seen the atomic PDF is simply another representation of the diffraction data; however, exploring the experimental data in real space is advantageous and helpful for several reasons, especially in the case of materials with significant structural disorder. First, as eq. 1 implies the total, not only the Bragg diffracted, intensities contribute to the PDF. In this way both the average, long-range atomic structure, manifested in the well-defined Bragg peaks, and the local structural imperfections, manifested in the diffuse components of the diffraction pattern, are projected in the PDF. Note that conventional crystallographic studies take only the Bragg peaks into account. Second, the PDF is barely influenced by diffraction optics and experimental factors since these are accounted for in the step of normalizing the raw diffraction data and converting it to S(Q) data [1]. This renders the PDF a sensitive structure-dependent quantity giving directly the relative positions of atoms in materials. Third, by accessing high values of Q, experimental PDF’s with high real-space resolution can be obtained and, hence,
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