Begin your search of the AGOSR Open Access Database
Cover Image for System.Linq.Enumerable+EnumerablePartition`1[System.Char]

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

OAI: oai:purehost.bath.ac.uk:publications/cc537799-cfb5-4909-9ee5-16096dea9d9b • DOI: https://doi.org/10.1107/S2053273319000615
Published by:

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.