From Finite to Infinite Range Order via Annealing: The Causal Architecture of Deformation Faulting in Annealed Close-Packed Crystals

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 layers carry structurally significant information and so layer stacking cannot be completely described by any finite-range Markov process. We compare our results to two experimental diffraction spectra, finding excellent agreement.Comment: 7 pages, 6 figures; See http://www.santafe.edu/projects/CompMech/papers/iro.htm

Chaotic Crystallography: How the physics of information reveals structural order in materials

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 approach relates to well known crystallographic practice and examine how it provides novel interpretations of familiar structures. Throughout, we concentrate on disordered materials that, while important, have received less attention both theoretically and experimentally than those with either periodic or aperiodic order.Comment: 9 pages, two figures, 1 table; http://csc.ucdavis.edu/~cmg/compmech/pubs/ChemOpinion.ht

Language extraction from ZnS

Perhaps the most fundamental questions we can ask about a solid are What is it made of? and How are the constituent parts assembled? This is so elementary, and yet so basic to any detailed understanding of the thermal, electrical, magnetic, optical, and elastic properties of materials. At the beginning of the twenty-first century, concern over the placement of the atoms in a solid seems quaint and anachronistic, more suited to the dawn of the twentieth century. X-ray diffraction, electron diffraction, optical microscopy, x-ray diffraction tomography, to name a few, are powerful techniques to uncover structure in solids. With this arsenal of tools, and the efforts of many researchers, surely we can have nothing novel to say about the discovery and description of structure in solids, save perhaps the refinement of well-worn techniques or the analysis of particularly obstinate cases. But careful examination of present technology reveals that while we are quite good at finding and describing periodic order in nature, cases that lack such order are much more difficult. Certainly in the complete absence of structural order, as in a gas, statistical methods exist that permit a satisfying understanding of the properties of the system without knowing ( or even wanting to know) the details of the microscopic placement of the constituents. But it is the in-between cases, where order and disorder coexist, that has proven so elusive to both analyze and describe. In this thesis, we will tackle these in-between cases for a special type of layered material, called polytypes. They exhibit disorder in one dimension only, making the analysis more tractable. We will give a method for determining the structure of these solids from experimental data and demonstrate how this structure, both the random and the non-random part, can be compactly expressed. From our solution, we will be able to calculate the effective range of the inter-layer interactions, as well as the configurational energies of the disordered stacking sequences

Islands in the Gap: Intertwined Transport and Localization in Structurally Complex Materials

Localized waves in disordered one-dimensional materials have been studied for decades, including white-noise and correlated disorder, as well as quasi-periodic disorder. How these wave phenomena relate to those in crystalline (periodic ordered) materials---arguably the better understood setting---has been a mystery ever since Anderson discovered disorder-induced localization. Nonetheless, together these revolutionized materials science and technology and led to new physics far beyond the solid state. We introduce a broad family of structurally complex materials---chaotic crystals---that interpolate between these organizational extremes---systematically spanning periodic structures and random disorder. Within the family one can tune the degree of disorder to sweep through an intermediate structurally disordered region between two periodic lattices. This reveals new transport and localization phenomena reflected in a rich array of energy-dependent localization degree and density of states. In particular, strong localization is observed even with a very low degree of disorder. Moreover, markedly enhanced localization and delocalization coexist in a very narrow range of energies. Most notably, beyond the simply smoothed bands found in previous disorder studies, islands of transport emerge in band gaps and sharp band boundaries persist in the presence of substantial disorder. Finally, the family of materials comes with rather direct specifications of how to assemble the requisite material organizations.Comment: 7 pages, 3 figures, supplementary material; http://csc.ucdavis.edu/~cmg/compmech/pubs/talisdm.ht

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide

In the previous paper of this series [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Physical Review B, submitted] we detailed a procedure--epsilon-machine spectral reconstruction--to discover and analyze patterns and disorder in close-packed structures as revealed in x-ray diffraction spectra. We argued that this computational mechanics approach is more general than the current alternative theory, the fault model, and that it provides a unique characterization of the disorder present. We demonstrated the efficacy of computational mechanics on four prototype spectra, finding that it was able to recover a statistical description of the underlying modular-layer stacking using epsilon-machine representations. Here we use this procedure to analyze structure and disorder in four previously published zinc sulphide diffraction spectra. We selected zinc sulphide not only for the theoretical interest this material has attracted in an effort to develop an understanding of polytypism, but also because it displays solid-state phase transitions and experimental data is available.Comment: 15 pages, 14 figures, 4 tables, 57 citations; http://www.santafe.edu/projects/CompMech/papers/ipdcpsii.htm

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: epsilon-Machine Spectral Reconstruction Theory

In a recent publication [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Phys. Rev. B {\bf 66}:17, 156 (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 give a detailed analysis of the current alternative approach, the fault model (FM), and offer several criticisms. We then demonstrate that the computational mechanics description of the stacking sequence--in the form of an epsilon-machine--provides the minimal and unique description of the crystal, whether ordered, disordered, or some combination. We find that we can detect and describe any amount of disorder, as well as materials that are mixtures of various kinds of crystalline structure. Underlying this approach is a novel method for epsilon-machine reconstruction that uses correlation functions estimated from diffraction spectra, rather than sequences of microscopic configurations, as is typically used in other domains. The result is that the methods developed here can be adapted to a wide range of experimental systems in which spectroscopic data is available.Comment: 26 pages, 23 figures, 8 tables, 110 citations; http://www.santafe.edu/projects/CompMech/papers/ipdcpsi.htm