A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene

Allen Hart; Thomas C. Hansen; Werner F. Kuhs

doi:10.1107/S2053273319000615

A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene

Allen Hart, Thomas C. Hansen, Werner F. Kuhs

Institut Laue Langevin

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Abstract

A mathematical framework is presented to represent turbostratic disorder in materials like carbon blacks, smectites and twisted n-layer graphene. In particular, the set of all possible disordered layers, including rotated, shifted and curved layers, forms a stochastic sequence governed by a hidden Markov model. The probability distribution over the set of layer types is treated as an element of a Hilbert space and, using the tools of Fourier analysis and functional analysis, expressions are developed for the scattering cross sections of a broad class of disordered materials.

Original language	English
Pages (from-to)	501-516
Number of pages	16
Journal	Acta Crystallographica Section A: Foundations and Advances
Volume	75
Issue number	3
Early online date	10 Apr 2019
DOIs	https://doi.org/10.1107/S2053273319000615
Publication status	Published - 1 May 2019

Keywords

Carbon blacks
Hidden Markov model
Scattering cross sections
Turbostratic disorder

ASJC Scopus subject areas

Structural Biology
Biochemistry
General Materials Science
Condensed Matter Physics
Physical and Theoretical Chemistry
Inorganic Chemistry

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Hart_et_al-2019-Acta_Crystallographica_Section_A.PDF
This is the final published version of an article published in Hart, A, Hansen, TC & Kuhs, WF 2019, 'A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene', Acta Crystallographica Section A: Foundations and Advances, vol. 75, no. 3, pp. 501-516 and available online via: https://doi.org/10.1107/S2053273319000615
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A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene

Abstract

Keywords

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