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

A previous paper detailed a novel algorithm, ɛ‐machine spectral reconstruction theory (ɛMSR), 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 ɛMSR 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, ɛMSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an ɛ‐machine. For stacking structures with a memory length larger than three, ɛMSR 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 ɛMSR 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 ɛ‐machine, and their relevance is discussed.