• 文献标题:   A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene
  • 文献类型:   Article
  • 作  者:   HART AG, HANSEN TC, KUHS WF
  • 作者关键词:   turbostratic disorder, carbon black, hidden markov model, scattering cross section
  • 出版物名称:   ACTA CRYSTALLOGRAPHICA AFOUNDATION ADVANCES
  • ISSN:   2053-2733
  • 通讯作者地址:   Univ Bath
  • 被引频次:   0
  • DOI:   10.1107/S2053273319000615
  • 出版年:   2019

▎ 摘  要

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.