Inferring planar disorder in close-packed structures via ε-machine spectral reconstruction theory: Examples from simulated diffraction patterns Dowman P. Varn Complexity Sciences Center & Physics Department, University of California, Davis Santa Fe Institute Department of Physics and Astromony, University of Tennessee, Knoxville Geoffrey S. Canright Telenor Research and Development Department of Physics and Astronomy, University of Tennessee, Knoxville James P. Crutchfield Complexity Sciences Center & Physics Department, University of California, Davis Santa Fe Institute Abstract: Previously we detailed a novel algorithm, ε-machine spectral reconstruction theory (εMSR), that infers pattern and disorder in planar-faulted, close-packed structures directly from X-ray diffraction patterns [Varn, et. al., (2013) Acta Crystallographica A, 69(2), pp. 197-206]. Here we apply εMSR to simulated diffraction patterns from four close-packed crystals. We find that for stacking structures with a memory length of three or less, εMSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an ε-machine. For stacking structures with a memory length larger than three, εMSR returns a model that captures many important features of the original stacking structure. These include multiple stacking faults and multiple crystal structures. Further, we find that εMSR is able to discover stacking structure in even highly disordered crystals. In order to address issues concerning the long range order observed in many classes of layered materials, we define several length parameters calculable from the ε-machine and discuss their relevance. A copy of this paper in pdf format: Inferring planar disorder in close-packed structures via ε-machine spectral reconstruction theory: Examples from simulated diffraction spectra Citation: DP Varn, GS Canright & JP Crutchfield, Acta Crystallographica Section A: Foundations of Crystallography 69(4) (2013) 413-426. Referee Reports