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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.

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