Inferring planar disorder in close-packed structuresvia∊-machine spectral reconstruction theory: examples from simulated diffraction patterns

Abstract

A previous paper 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 Cryst. A69, 197-206]. Here εMSR is applied to simulated diffraction patterns from four close-packed crystals. It is found 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, it is found 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, several length parameters are defined, calculable from the ε-machine, and their relevance is discussed.

Pairwise correlations in layered close-packed structures

“…In analyzing a broad range of CFs, nevertheless, many authors have been led to consider correlation lengths, also known as characteristic lengths (Tiwary & Pandey, 2007;Varn et al, 2013b). The form of equation (20) suggests that this perspective will often be a clumsy oversimplification for understanding CFs.…”

“…Let us consider a CPS stacked according to the Golden Mean (GM) process (Crutchfield & Feldman, 2003). The GM process has been previously treated in the context of CPSs in Varn (2013b). The GM process is generically defined as follows: any sequence is allowed as long as there are no consecutive 0's.…”

Chaotic crystallography: how the physics of information reveals structural order in materials

“…of the reconstruction methods available in computational mechanics, such as the subtree merging method [25], causal state splitting reconstruction [56] or Bayesian structural inference [57], to find the appropriate model [44]. (iii) Lastly, the approach that has received the most attention is ε-machine spectral reconstruction theory (εMSR) [34,43,45,46]. The importance of this technique is that it uses experimentally obtained X-ray diffraction patterns to reconstruct the stacking process ε-machine.…”

“…εMSR [34,43,45,46] employs Fourier analysis over a unit interval in frequency space to extract information about the pairwise correlations between the MLs and then solves a set of equations for sequence probabilities. The algorithm initially considers low-order Markov processes and compares the diffraction pattern calculated from the model with the experimental one.…”

“…Chaotic crystallography (ChC) [21,34,[43][44][45][46][47] is the application of information-and computation-theoretic methods to discover and characterize structure in materials. The choice of the name is intended to be evocative: we retain the term 'crystallography' to emphasize continuity with past goals of understanding material structure; and we introduce the term 'chaotic' to associate this new approach with notions of disorder, complexity, and information processing.…”