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
