| Dowman P. Varn Complexity Sciences Center Physics Department University of California at Davis Davis, CA 95616, USA | Geoffrey S. Canright Telenor Research and Development 1331 Fornebu, Norway |
James P. Crutchfield Complexity Sciences Center Physics Department University of California at Davis Davis, CA 95616, USA |
ABSTRACT: Previously we detailed a novel algorithm, ε-machine spectral reconstruction theory (ε-MSR), that infers pattern and disorder in planar-faulted, close-packed struc- tures directly from X-ray diffraction patterns [Varn, et. al., (2013) Acta Crystallographica A]. 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.