  We present a mathematical framework 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 form 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 tools of Fourier analysis
and functional analysis, we develop expressions for the scattering cross
sections of a broad class of disordered materials.

Chemical Physics