Inferring Pattern and Disorder in Close-Packed Structures via $\epsilon$-Machine Reconstruction Theory: Examples from Simulated Diffraction Spectra

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: Previously we detailed a novel algorithm, epsilon-machine spectral reconstruction theory (eMSR), that infers pattern and disorder in planar-faulted, close-packed structures directly from X-ray diffraction spectra [Varn, Canright and Crutchfield, to appear in Acta Crystallographica A. Here we apply eMSR to simulated diffraction spectra from five close-packed crystals. We find that for stacking structures with a memory length of three or less, eMSR reproduces the statistics of the stacking structure; the result being in the form of a directed graph called an epsilon-machine. For stacking structures with a memory length larger than three, eMSR returns a model that captures many important features of the original stacking structure. These include multiple stacking faults and multiple crystal structures. Further, we find that eMSR is able to discover stacking structurein even highly disordered crystals. In order to address issues concerning the long range order observed in many classes of layered materials, we define several length parameters calculable from the epsilon-machine, and discuss their relevance.


D. P. Varn, G. S. Canright, and J. P. Crutchfield, " Inferring Pattern and Disorder in Close-Packed Structures via $\epsilon$-Machine Reconstruction Theory: Examples from Simulated Diffraction Spectra", Acta Crystallographica Section A (2006) in press. [pdf] = 357 kb.