A hidden Markov model for describing turbostratic disorder applied to carbon blacks and graphene
2019 ◽
Vol 75
(3)
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pp. 501-516
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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.
2007 ◽
Vol 11
(6)
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pp. 662-667
2017 ◽
Vol 10
(4)
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pp. 239
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2012 ◽
Vol 2
(6)
◽
pp. 208-211
2012 ◽
Vol 132
(10)
◽
pp. 1589-1594
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