ε-Machine Spectral Reconstruction Theory:
A direct method for inferring planar disorder and structure from X-ray diffraction studies

Dowman P. Varn
Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616, USA
Geoffrey S. Canright
Telenor Research and Development
1331 Fornebu, Norway


James P. Crutchfield
Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616, USA

ABSTRACT: In previous publications [Phys. Rev. B 66 174110 (2002), Acta Crystallogr. B 63:2 (2006) 169-182] we introduced and applied a new technique for discovering and describing planar disorder in close-packed structures directly from their diffrac- tion patterns. Here, we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in mate- rials. We show that the resulting statistical model of the stacking structure—called the ε-machine—allows the calculation of measures of memory, structural complexity, and configurational entropy. The methods developed here can be adapted to a wide range of experimental systems in which power spectra data are available.


D. P. Varn, G. S. Canright, and J. P. Crutchfield, "ε-Machine spectral reconstruction theory: A direct method for inferring planar disorder and structure from X-ray diffraction studies" Acta Crystallographica Section A 69:2 (2013) 197-206.
Santa Fe Institute Working Paper 03-03-021. [ps.gz] [ps] [pdf]. http://arXiv.org/abs/cond-mat/0302585.