Dark-field transmission electron microscopy and the Debye-Waller factor of graphene

Graphene's structure bears on both the material's electronic properties and fundamental questions about long range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multi-layer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multi-layer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary.Comment: 10 pages, 4 figure

Dark-field transmission electron microscopy and the Debye-Waller factor of graphene

Graphene\u27s structure bears on both the material\u27s electronic properties and fundamental questions about long-range order in two-dimensional crystals. We present an analytic calculation of selected area electron diffraction from multilayer graphene and compare it with data from samples prepared by chemical vapor deposition and mechanical exfoliation. A single layer scatters only 0.5% of the incident electrons, so this kinematical calculation can be considered reliable for five or fewer layers. Dark-field transmission electron micrographs of multilayer graphene illustrate how knowledge of the diffraction peak intensities can be applied for rapid mapping of thickness, stacking, and grain boundaries. The diffraction peak intensities also depend on the mean-square displacement of atoms from their ideal lattice locations, which is parameterized by a Debye-Waller factor. We measure the Debye-Waller factor of a suspended monolayer of exfoliated graphene and find a result consistent with an estimate based on the Debye model. For laboratory-scale graphene samples, finite size effects are sufficient to stabilize the graphene lattice against melting, indicating that ripples in the third dimension are not necessary

Direct Identification of Monolayer Rhenium Diselenide by an Individual Diffraction Pattern

In the current extensive studies of transition metal dichalcogenides (TMDCs), compared to hexagonal layered materials, like graphene, hBN and MoS2, low symmetry layered two‐dimensional (2D) crystals have shown great potential for applications in anisotropic devices. Rhenium diselenide (ReSe2) has the bulk space group P1ത and belongs to triclinic crystal system with a deformed cadmium iodide type structure. Here we propose an electron diffraction based method to distinguish monolayer ReSe2 membrane from multilayer ReSe2, and its two different vertical orientations, our method could also be applicable to other low symmetry crystal systems, including both triclinic and monoclinic lattices, as long as their third unit‐cell basis vectors are not perpendicular to their basal planes. Our experimental results are well explained by kinematical electron diffraction theory and corresponding simulations. The generalization of our method to other 2D materials, like graphene, is also discussed

Self-assembly and metal-directed assembly of organic semiconductor aerogels and conductive carbon nanofiber aerogels with controllable nanoscale morphologies

A versatile and highly tunable synthesis for nanofiber aerogels based on the n-type organic semiconductor perylene tetracarboxylic diimide (PTCDI) is presented. PTCDI nanofiber aerogels are demonstrated to incorporate the organic semiconductor into a high surface area and porous morphology, and can also be graphitized to synthesize carbon nanofiber (CNF) aerogels by thermal annealing. Using this approach, CNF aerogels with variable density and crystallinity are synthesized. Furthermore, by incorporating metal salts into the synthesis, metal-directed assembly yields a variety of nanoscale morphologies. The selection of post-synthesis thermal treatment can result in metal-directed assembly of PTCDI aerogels, low crystallinity graphitic aerogels decorated with metal nanoparticles, or highly crystalline graphitic aerogels with controllable nanoscale morphologies. The high surface area and porosity afforded by the aerogel morphology coupled with the intrinsic properties of PTCDI or CNFs is important for improving their performance in a number of applications including energy storage and catalysis