Diffraction Patterns of Layered Close-packed Structures from Hidden Markov Models
Skip to main content
eScholarship
Open Access Publications from the University of California

Diffraction Patterns of Layered Close-packed Structures from Hidden Markov Models

  • Author(s): Riechers, P. M.
  • Varn, D. P.
  • Crutchfield, J. P.
  • et al.

Published Web Location

https://arxiv.org/pdf/1410.5028.pdf
No data is associated with this publication.
Abstract

We recently derived analytical expressions for the pairwise (auto)correlation functions (CFs) between modular layers (MLs) in close-packed structures (CPSs) for the wide class of stacking processes describable as hidden Markov models (HMMs) [Riechers \etal, (2014), Acta Crystallogr.~A, XX 000-000]. We now use these results to calculate diffraction patterns (DPs) directly from HMMs, discovering that the relationship between the HMMs and DPs is both simple and fundamental in nature. We show that in the limit of large crystals, the DP is a function of parameters that specify the HMM. We give three elementary but important examples that demonstrate this result, deriving expressions for the DP of CPSs stacked (i) independently, (ii) as infinite-Markov-order randomly faulted 2H and 3C stacking structures over the entire range of growth and deformation faulting probabilities, and (iii) as a HMM that models Shockley-Frank stacking faults in 6H-SiC. While applied here to planar faulting in CPSs, extending the methods and results to planar disorder in other layered materials is straightforward. In this way, we effectively solve the broad problem of calculating a DP---either analytically or numerically---for any stacking structure---ordered or disordered---where the stacking process can be expressed as a HMM.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Item not freely available? Link broken?
Report a problem accessing this item