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

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

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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
Issue number3
Early online date10 Apr 2019
Publication statusPublished - 1 May 2019


  • 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

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