Characterizing the Turbostratic Disorder in COF-5 with NMR Crystallography

Since its initial synthesis in 2005, COF-5 has been known to have intrinsic disorder in the placement of the 2D layers relative to one another (i.e. turbostratic disorder). Prior studies of have demonstrated that the eclipsed layering found in the space group originally assigned to COF-5 (<i>P</i>6<i>/mmm</i>) is inconsistent with energy considerations. Herein it is demonstrated that eclipsed layers are also inconsistent with¹³C solid-state NMR data. Crystal structure predictions are made in five alternative space groups and good agreement is obtained in <i>P</i>21<i>/m</i>, <i>Cmcm</i>, and <i>C</i>2<i>/m</i>. We posit that all three space groups are present within the stacked 2D layers and show that this conclusion is consistent with evidence from ¹³C solid-state NMR linewidths and chemical shifts, powder x-ray diffraction data and energy considerations. An alternative explanation involving a mixture of multiple pure phases is rejected because the observed NMR spectra don’t exhibit the characteristic features of such mixed phase materials.

Characterizing the Turbostratic Disorder in COF-5 with NMR Crystallography

Since its initial synthesis in 2005, COF-5 has been known to have intrinsic disorder in the placement of the 2D layers relative to one another (i.e. turbostratic disorder). Prior studies of have demonstrated that the eclipsed layering found in the space group originally assigned to COF-5 (<i>P</i>6<i>/mmm</i>) is inconsistent with energy considerations. Herein it is demonstrated that eclipsed layers are also inconsistent with¹³C solid-state NMR data. Crystal structure predictions are made in five alternative space groups and good agreement is obtained in <i>P</i>21<i>/m</i>, <i>Cmcm</i>, and <i>C</i>2<i>/m</i>. We posit that all three space groups are present within the stacked 2D layers and show that this conclusion is consistent with evidence from ¹³C solid-state NMR linewidths and chemical shifts, powder x-ray diffraction data and energy considerations. An alternative explanation involving a mixture of multiple pure phases is rejected because the observed NMR spectra don’t exhibit the characteristic features of such mixed phase materials.

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

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.

Thermal evolution of Mg–Al and Ni–Al layered double hydroxides: the structure of the dehydrated phase

Simulation of X-ray diffraction patterns on the basis of the models of one-dimensional disordered crystals was used to investigate the structure of the dehydrated phase produced by dehydration of Mg–Al and Ni–Al layered double hydroxides at a temperature of ∼473–498 K. It was found that the removal of water molecules transforms the initial structure, which is a mixture of 3R1and 2H1polytypes, into a structure that comprises preferentially fragments of 3R2and 1Hpolytypes and has some turbostratic disorder.

Description of X-ray powder pattern of turbostratically disordered layer structures with a Rietveld compatible approach

We address the problem of the quantitative description of X-ray powder pattern of turbostratically disordered layer compounds. The Debye formula is used, which allows the aperiodic description of any arrangement of atoms. With the extension of Yang and Frindt (1996) for the ideal turbostratic case, these calculations are used to generate reference data that are subsequently treated by the Rietveld method. We are able to show that the case of uncorrelated turbostratic disorder can be modelled equally well in a periodic supercell approach with a single layer in the supercell that is suitable for the Rietveld technique. A brief introduction of this new model was given as an oral contribution at EUROCLAY 2003 (Ufer et al., 2003). The fundamental principles are described in this article because of its complexity. The applicability of this approach to real systems is demonstrated for smectite and corundum mixtures.

Turbostratic Disorder in [(Bi2Te3)x(TiTe2)y] Superlattices

ABSTRACTA family of metastable [(Bi2Te3)x(TiTe2)y] superlattices (where × and y denote the number of layers of each of the two components) was prepared by annealing modulated elemental reactant precursors at temperatures below 280°C. Structural analysis by traditional XRD shows the superlattice structures are highly aligned to the substrate with many orders of diffraction peaks from the c direction of the superlattice. Off-axis diffraction techniques presented in this paper suggest that the order between the layers in the a-b direction of these superlattice structures is turbostratic. In this type of behavior, the quasi two-dimensional crystals of Bi2Te3 and TiTe2 that comprise the superlattice structure lie like a deck of cards thrown in disarray on a surface. An analysis of the diffraction data leading to this conclusion is given.