A hidden Markov model for describing turbostratic disorder 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.

Polymorphs and solid solutions: materials with new luminescent properties obtained through mechanochemical transformation of dicyanoaurate(i) salts

“…Turbostratic disorder has been extensively studied due to the impact on lithium intercalation and electrical conductivity in graphite. 68–70…”

“…Turbostratic disorder has been extensively studied due to the impact on lithium intercalation and electrical conductivity in graphite. [68][69][70] In a simple, preliminary attempt to validate the effect of such potential turbostratic disorder on the PXRD pattern of the material, we have articially distorted the periodicity of the KAu(CN) 2 structure in the ab-plane by shiing all atoms in a single layer of gold atoms by 20% along the crystallographic b-axis. While this transformation, which does not represent a reasonable structure, did not affect the (003), (006) and (009) X-ray reections in the calculated PXRD pattern, the intensities of other X-ray reections have dropped signicantly.…”