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

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

Research output: Contribution to journalArticle

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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 languageEnglish
Pages (from-to)501-516
Number of pages16
JournalActa Crystallographica Section A: Foundations and Advances
Volume75
Issue number3
Early online date10 Apr 2019
DOIs
Publication statusPublished - 1 May 2019

Keywords

  • Carbon blacks
  • Hidden Markov model
  • Scattering cross sections
  • Turbostratic disorder

ASJC Scopus subject areas

  • Structural Biology
  • Biochemistry
  • Materials Science(all)
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry

Cite this

A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene. / Hart, Allen; Hansen, Thomas C.; Kuhs, Werner F.

In: Acta Crystallographica Section A: Foundations and Advances, Vol. 75, No. 3, 01.05.2019, p. 501-516.

Research output: Contribution to journalArticle

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