A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene. Issue 3 (10th April 2019)

• Record Type: Journal Article
• Authors: Hart, Allen G.; Hansen, Thomas C.; Kuhs, Werner F.
• Is Part Of: Acta crystallographica. Volume 75:Issue 3(2019:May)
• Page Start: 501
• Page End: 516
• Publication Date: 2019-04-10
• Subjects: turbostratic disorder -- carbon blacks -- hidden Markov model -- scattering cross sections; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S2053273319000615
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : A mathematical framework for analysing aperiodic crystals encompassing a wide range of turbostratic disorders, including disorder of the first and second type, is presented. The framework uses the theory of hidden Markov models and is applied to carbon blacks and graphene. 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.