| Dowman P. Varn Max-Planck-Institut fur Physik Komplexer Systeme Nothnitzer Strasse 38 01187 Dresden, Germany |
Geoffrey S. Canright Department of Physics and Astronomy University of Tennessee Knoxville, Tennessee 37996, USA and Telenor Research and Development 1331 Fornebu, Olso, Norway |
James P. Crutchfield Center for Computational Science and Engineering Physics DepartmenEngineering University of California, Davis One Shields Avenue Davis, CA 95616, USA |
ABSTRACT: In a recent publication [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Phys. Rev. B 66:17, 156 (2002)] we introduced a new technique for discovering and describing planar disorder in close-packed structures directly from their diffraction spectra. Here we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials. We show that the resulting statistical model of the stacking structure---called the epsilon-machine---allows the calculation of measures of memory, structural complexity, and configurational entropy. By way of contrast, we give a detailed analysis of the current alternative approach, the fault model, and offer several criticisms. In the limit of weak faulting, we demonstrate how various architectural features of the epsilon-machine correspond to well-known structural faults in two common types of crystal, 2H and 3C. The methods developed here can be adapted to a wide range of experimental systems in which spectroscopic data is available.