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We solve a long-standing problem—determining structural information for disordered materials from their diffraction spectra—for the special case of planar disorder in close-packed structures (CPSs). Our solution offers the most complete possible statistical description of the disorder and, from it, we find the minimum effective memory length for stacking… (More)

We analyze solid-state phase transformations that occur in zinc-sulfide crystals during annealing using a random deformation-faulting mechanism with a very simple interaction between adjacent close-packed double layers. We show that, through annealing, infinite-range structures emerge from initially short-range crystal order. That is, widely separated… (More)

We review recent progress in applying information-and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for this new toolset and show how the new techniques detect and describe novel material properties. We discuss how the… (More)

- Dowman P Varn, D P Iv [ † ] Varn, G S Canright, J P Crutchfield, Varn, D P Varn +32 others

This thesis represents the first formal presentation of the algorithm for-machine reconstruction from spectral data called-machine spectral reconstruction theory or MSR. As might be expected from a work that introduces a novel approach—let alone one that is written by a student to satisfy the requirements of a degree—there is significant attention given to… (More)

Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, analytical expressions are developed for the pairwise correlation functions between the layers. These may be calculated analytically as explicit functions of model parameters or the expressions may be used as a fast, accurate and efficient… (More)

We develop a method to calculate the diffraction pattern for layered close-packed structures stacked according to the wide class of processes expressible as hidden Markov models. We show that in the limit of large crystals, the diffraction pattern is a particularly simple function of parameters that specify the hidden Markov model. We give three elementary… (More)

Previously we detailed a novel algorithm,-machine spectral reconstruction theory (MSR), that infers pattern and disorder in planar-faulted, close-packed structures directly from X-ray diffraction patterns [Varn, et. al., (2013) Acta Crystal-lographica A]. Here we apply MSR to simulated diffraction patterns from four close-packed crystals. We find that for… (More)

Erwin Schrödinger famously and presciently ascribed the vehicle transmitting the hereditary information underlying life to an 'aperiodic crystal'. We compare and contrast this, only later discovered to be stored in the linear biomolecule DNA, with the information-bearing, layered quasi-one-dimensional materials investigated by the emerging field of chaotic… (More)

- P M Riechers, D P Varn, J P Crutchfield
- 2014

SFI Working Papers contain accounts of scienti5ic work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-‐reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work… (More)

In a recent publication [ (2002)] we introduced a new technique for discovering and describing planar disorder in close-packed structures (CPSs) directly from their diffraction spectra. Here we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials. By way of contrast, we… (More)