Representational Analysis of Extended Disorder in Crystals from Total Scattering Data

James R. Neilson (Department of Chemistry, Colorado State University)

With the increased availability of synchrotron X-ray and time-of-flight neutron diffraction data that access large regions of momentum transfer, pair distribution function analysis is becoming a standard technique for the study of disorder in crystalline solids. For many materials, it is intractable to directly compare a structure generated from "small-box" modeling of the pair distribution function with a structural model obtained from traditional crystallography: the challenge is to define an atomistic structure that equivalently describes both the average crystallographic symmetry and the local coordination. Simultaneous simulations of the diffraction data and the pair distribution function are feasible with the Reverse Monte Carlo (RMC) method using large atomistic ensembles. However, extraction of meaningful and robust information from these large configurations with thousands of degrees of freedom is non-trivial. Using representational analysis, it is possible to rewrite the displacements in terms of a local basis derived from the average crystallographic symmetry that advantageously describes to the lattice connectivity. By writing the atom displacements in terms of the irreducible representations, it is possible to use higher-order spectral analysis (the bispectrum) to extract meaningful atomic displacements across hundreds of individual simulations. This robust approach provides direct and new insight into the chemistry and physics of myriad complex crystalline solids that are often inaccessible with traditional Rietveld analysis.

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